In this article, we consider a lifetime distribution, the Weibull-Logarithmic distri- bution introduced by [6]. We investigate some new statistical characterizations and properties. We develop the maximum likelihood i...In this article, we consider a lifetime distribution, the Weibull-Logarithmic distri- bution introduced by [6]. We investigate some new statistical characterizations and properties. We develop the maximum likelihood inference using EM algorithm. Asymptotic properties of the MLEs are obtained and extensive simulations are conducted to assess the performance of parameter estimation. A numerical example is used to illustrate the application.展开更多
Weighted exponential distribution W ED(α,λ)with shape parameterαand scale parameterλpossesses some good properties and can be used as a good fit to survival time data compared to other distributions such as gamma,...Weighted exponential distribution W ED(α,λ)with shape parameterαand scale parameterλpossesses some good properties and can be used as a good fit to survival time data compared to other distributions such as gamma,Weibull,or generalized exponential distribution.In this article,we proved the existence and uniqueness of the maximum likelihood estimator(MLE)of the parameters of W ED(α,λ)in simple random sampling(SRS)and provided explicit expressions for the Fisher information number in SRS.Moreover,we also proved the existence and uniqueness of the MLE of the parameters of W ED(α,λ)in ranked set sampling(RSS)and provided explicit expressions for the Fisher information number in RSS.Simulation studies show that these MLEs in RSS can be real competitors for those in SRS.展开更多
Over the past few decades, numerous adaptive Kalman filters(AKFs) have been proposed. However, achieving online estimation with both high estimation accuracy and fast convergence speed is challenging, especially when ...Over the past few decades, numerous adaptive Kalman filters(AKFs) have been proposed. However, achieving online estimation with both high estimation accuracy and fast convergence speed is challenging, especially when both the process noise and measurement noise covariance matrices are relatively inaccurate. Maximum likelihood estimation(MLE) possesses the potential to achieve this goal, since its theoretical accuracy is guaranteed by asymptotic optimality and the convergence speed is fast due to weak dependence on accurate state estimation.Unfortunately, the maximum likelihood cost function is so intricate that the existing MLE methods can only simply ignore all historical measurement information to achieve online estimation,which cannot adequately realize the potential of MLE. In order to design online MLE-based AKFs with high estimation accuracy and fast convergence speed, an online exploratory MLE approach is proposed, based on which a mini-batch coordinate descent noise covariance matrix estimation framework is developed. In this framework, the maximum likelihood cost function is simplified for online estimation with fewer and simpler terms which are selected in a mini-batch and calculated with a backtracking method. This maximum likelihood cost function is sidestepped and solved by exploring possible estimated noise covariance matrices adaptively while the historical measurement information is adequately utilized. Furthermore, four specific algorithms are derived under this framework to meet different practical requirements in terms of convergence speed, estimation accuracy,and calculation load. Abundant simulations and experiments are carried out to verify the validity and superiority of the proposed algorithms as compared with existing state-of-the-art AKFs.展开更多
A Bayesian approach using Markov chain Monte Carlo algorithms has been developed to analyze Smith’s discretized version of the discovery process model. It avoids the problems involved in the maximum likelihood method...A Bayesian approach using Markov chain Monte Carlo algorithms has been developed to analyze Smith’s discretized version of the discovery process model. It avoids the problems involved in the maximum likelihood method by effectively making use of the information from the prior distribution and that from the discovery sequence according to posterior probabilities. All statistical inferences about the parameters of the model and total resources can be quantified by drawing samples directly from the joint posterior distribution. In addition, statistical errors of the samples can be easily assessed and the convergence properties can be monitored during the sampling. Because the information contained in a discovery sequence is not enough to estimate all parameters, especially the number of fields, geologically justified prior information is crucial to the estimation. The Bayesian approach allows the analyst to specify his subjective estimates of the required parameters and his degree of uncertainty about the estimates in a clearly identified fashion throughout the analysis. As an example, this approach is applied to the same data of the North Sea on which Smith demonstrated his maximum likelihood method. For this case, the Bayesian approach has really improved the overly pessimistic results and downward bias of the maximum likelihood procedure.展开更多
In order to obtain the life information of the vacuum fluorescent display （VFD） in a short time, a model of constant stress accelerated life tests （CSALT） is established with its filament temperature increased, an...In order to obtain the life information of the vacuum fluorescent display （VFD） in a short time, a model of constant stress accelerated life tests （CSALT） is established with its filament temperature increased, and four constant stress tests are conducted. The Weibull function is applied to describe the life distribution of the VFD, and the maximum likelihood estimation （MLE） and its iterative flow chart are used to calculate the shape parameters and the scale parameters. Furthermore, the accelerated life equation is determined by the least square method, the Kolmogorov-Smirnov test is performed to verify whether the VFD life meets the Weibull distribution or not, and selfdeveloped software is employed to predict the average life and the reliable life. Statistical data analysis results demonstrate that the test plans are feasible and versatile, that the VFD life follows the Weibull distribution, and that the VFD accelerated model satisfies the linear Arrhenius equation. The proposed method and the estimated life information of the VFD can provide some significant guideline to its manufacturers and customers.展开更多
随着风电渗透率的持续上升,电力系统的惯量水平显著下降,对系统频率稳定性构成了新的挑战。为有效评估风电并网情况下电力系统节点惯量的变化,提出了一种基于受控自回归滑动平均(autoregressive moving average with exogenous variable...随着风电渗透率的持续上升,电力系统的惯量水平显著下降,对系统频率稳定性构成了新的挑战。为有效评估风电并网情况下电力系统节点惯量的变化,提出了一种基于受控自回归滑动平均(autoregressive moving average with exogenous variable,ARMAX)模型的改进最大似然估计(maximum likelihood estimation,MLE)参数辨识方法对系统机组直接相连节点进行惯量评估。首先,构建ARMAX模型对发电机组直接相连节点的动态特性进行建模,并利用改进MLE对模型参数进行辨识,以评估与机组直接相连的节点惯量。然后,基于k-means聚类算法对发电机组节点惯量进行分区,计算得到系统区域惯量和中心频率,并进一步对非发电机组节点频率进行自适应多项式拟合计算,得到其系统节点惯量。最后,搭建IEEE39含风力发电机组节点系统,绘制热力图直观展示电力系统节点和区域的惯量分布,验证了所提改进方法的有效性。该方法有助于精准识别系统中不同节点的动态响应特性,为风电并网系统的分析和规划提供了有力支持。展开更多
In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood e...In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.展开更多
To estimate the spreading sequence of the direct sequence spread spectrum(DSSS)signal,a fast algorithm based on maximum likelihood function is proposed,and the theoretical derivation of the algorithm is provided.By si...To estimate the spreading sequence of the direct sequence spread spectrum(DSSS)signal,a fast algorithm based on maximum likelihood function is proposed,and the theoretical derivation of the algorithm is provided.By simplifying the objective function of maximum likelihood estimation,the algorithm can realize sequence synchronization and sequence estimation via adaptive iteration and sliding window.Since it avoids the correlation matrix computation,the algorithm significantly reduces the storage requirement and the computation complexity.Simulations show that it is a fast convergent algorithm,and can perform well in low signal to noise ratio(SNR).展开更多
This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both ...This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.展开更多
A crowdsourcing experiment in which viewers (the “crowd”) of a British Broadcasting Corporation (BBC) television show submitted estimates of the number of coins in a tumbler was shown in an antecedent paper (Part 1)...A crowdsourcing experiment in which viewers (the “crowd”) of a British Broadcasting Corporation (BBC) television show submitted estimates of the number of coins in a tumbler was shown in an antecedent paper (Part 1) to follow a log-normal distribution ∧(m,s2). The coin-estimation experiment is an archetype of a broad class of image analysis and object counting problems suitable for solution by crowdsourcing. The objective of the current paper (Part 2) is to determine the location and scale parameters (m,s) of ∧(m,s2) by both Bayesian and maximum likelihood (ML) methods and to compare the results. One outcome of the analysis is the resolution, by means of Jeffreys’ rule, of questions regarding the appropriate Bayesian prior. It is shown that Bayesian and ML analyses lead to the same expression for the location parameter, but different expressions for the scale parameter, which become identical in the limit of an infinite sample size. A second outcome of the analysis concerns use of the sample mean as the measure of information of the crowd in applications where the distribution of responses is not sought or known. In the coin-estimation experiment, the sample mean was found to differ widely from the mean number of coins calculated from ∧(m,s2). This discordance raises critical questions concerning whether, and under what conditions, the sample mean provides a reliable measure of the information of the crowd. This paper resolves that problem by use of the principle of maximum entropy (PME). The PME yields a set of equations for finding the most probable distribution consistent with given prior information and only that information. If there is no solution to the PME equations for a specified sample mean and sample variance, then the sample mean is an unreliable statistic, since no measure can be assigned to its uncertainty. Parts 1 and 2 together demonstrate that the information content of crowdsourcing resides in the distribution of responses (very often log-normal in form), which can be obtained empirically or by appropriate modeling.展开更多
To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid sear...To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, thus its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an appropriate grid spacing adaptively, and is able to yield approximate maximum likelihood estimate （MLE） with a computational complexity of O（n2）. Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing methods. Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate similarly by grid search.展开更多
By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of ...By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of the identification parameters is given. In order to decrease the asymptotic error, a corrector of maximum likelihood (CML) estimation with its recursive algorithm is given. It has been proved that the corrector has smaller asymptotic error than the least square methods. A simulation example shows that the corrector of maximum likelihood estimation is of higher approximating precision to the true parameters than the least square methods.展开更多
In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression ...In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression model with exact linear restrictions. However, there are some situations, where the linear restrictions are stochastic. In this paper, we propose a Stochastic Restricted Maximum Likelihood Estimator (SRMLE) for the logistic regression model with stochastic linear restrictions to overcome this issue. Moreover, a Monte Carlo simulation is conducted for comparing the performances of the MLE, Restricted Maximum Likelihood Estimator (RMLE), Ridge Type Logistic Estimator(LRE), Liu Type Logistic Estimator(LLE), and SRMLE for the logistic regression model by using Scalar Mean Squared Error (SMSE).展开更多
Maximum likelihood estimation(MLE)is an effective method for localizing radioactive sources in a given area.However,it requires an exhaustive search for parameter estimation,which is time-consuming.In this study,heuri...Maximum likelihood estimation(MLE)is an effective method for localizing radioactive sources in a given area.However,it requires an exhaustive search for parameter estimation,which is time-consuming.In this study,heuristic techniques were employed to search for radiation source parameters that provide the maximum likelihood by using a network of sensors.Hence,the time consumption of MLE would be effectively reduced.First,the radiation source was detected using the k-sigma method.Subsequently,the MLE was applied for parameter estimation using the readings and positions of the detectors that have detected the radiation source.A comparative study was performed in which the estimation accuracy and time consump-tion of the MLE were evaluated for traditional methods and heuristic techniques.The traditional MLE was performed via a grid search method using fixed and multiple resolutions.Additionally,four commonly used heuristic algorithms were applied:the firefly algorithm(FFA),particle swarm optimization(PSO),ant colony optimization(ACO),and artificial bee colony(ABC).The experiment was conducted using real data collected by the Low Scatter Irradiator facility at the Savannah River National Laboratory as part of the Intelligent Radiation Sensing System program.The comparative study showed that the estimation time was 3.27 s using fixed resolution MLE and 0.59 s using multi-resolution MLE.The time consumption for the heuristic-based MLE was 0.75,0.03,0.02,and 0.059 s for FFA,PSO,ACO,and ABC,respectively.The location estimation error was approximately 0.4 m using either the grid search-based MLE or the heuristic-based MLE.Hence,heuristic-based MLE can provide comparable estimation accuracy through a less time-consuming process than traditional MLE.展开更多
In this paper a method of aerodynamic parameter identification of vehicle, the maximum likelihood method, is introduced. The aerodynamic model of vehicle is identified and the basic equations using maximum likelihood ...In this paper a method of aerodynamic parameter identification of vehicle, the maximum likelihood method, is introduced. The aerodynamic model of vehicle is identified and the basic equations using maximum likelihood method are established. After that, the simulation data is identified to verify the correctness of the mathematic model and identification method. Last, the practical flight data is identified and analyzed.展开更多
Low elevation estimation,which has attracted wide attention due to the presence of specular multipath,is essential for tracking radars.Frequency agility not only has the advantage of strong anti-interference ability,b...Low elevation estimation,which has attracted wide attention due to the presence of specular multipath,is essential for tracking radars.Frequency agility not only has the advantage of strong anti-interference ability,but also can enhance the performance of tracking radars.A frequency-agile refined maximum likelihood(RML)algorithm based on optimal fusion is proposed.The algorithm constructs an optimization problem,which minimizes the mean square error(MSE)of angle estimation.Thereby,the optimal weight at different frequency points is obtained for fusing the angle estimation.Through theoretical analysis and simulation,the frequency-agile RML algorithm based on optimal fusion can improve the accuracy of angle estimation effectively.展开更多
As a widely used reconstruction algorithm in quantum state tomography, maximum likelihood estimation tends to assign a rank-deficient matrix, which decreases estimation accuracy for certain quantum states. Fortunately...As a widely used reconstruction algorithm in quantum state tomography, maximum likelihood estimation tends to assign a rank-deficient matrix, which decreases estimation accuracy for certain quantum states. Fortunately, hedged maximum likelihood estimation （HMLE） [Phys. Rev. Lett. 105 （2010）200504] was proposed to avoid this problem. Here we study more details about this proposal in the two-qubit case and further improve its performance. We ameliorate the HMLE method by updating the hedging function based on the purity of the estimated state. Both performances of HMLE and ameliorated HMLE are demonstrated by numerical simulation and experimental implementation on the Werner states of polarization-entangled photons.展开更多
The conformal array can make full use of the aperture,save space,meet the requirements of aerodynamics,and is sensitive to polarization information.It has broad application prospects in military,aerospace,and communic...The conformal array can make full use of the aperture,save space,meet the requirements of aerodynamics,and is sensitive to polarization information.It has broad application prospects in military,aerospace,and communication fields.The joint polarization and direction-of-arrival(DOA)estimation based on the conformal array and the theoretical analysis of its parameter estimation performance are the key factors to promote the engineering application of the conformal array.To solve these problems,this paper establishes the wave field signal model of the conformal array.Then,for the case of a single target,the cost function of the maximum likelihood(ML)estimator is rewritten with Rayleigh quotient from a problem of maximizing the ratio of quadratic forms into those of minimizing quadratic forms.On this basis,rapid parameter estimation is achieved with the idea of manifold separation technology(MST).Compared with the modified variable projection(MVP)algorithm,it reduces the computational complexity and improves the parameter estimation performance.Meanwhile,the MST is used to solve the partial derivative of the steering vector.Then,the theoretical performance of ML,the multiple signal classification(MUSIC)estimator and Cramer-Rao bound(CRB)based on the conformal array are derived respectively,which provides theoretical foundation for the engineering application of the conformal array.Finally,the simulation experiment verifies the effectiveness of the proposed method.展开更多
The estimation of target parameters in MIMO radar signal processing is one of the most important research topics. An efficient implementation of the Maximum Likelihood estimator is presented in this paper to estimate ...The estimation of target parameters in MIMO radar signal processing is one of the most important research topics. An efficient implementation of the Maximum Likelihood estimator is presented in this paper to estimate the DOA (Direction of Arrival), initial velocity and acceleration of a maneuvering target in colocated MIMO radar. The target’s DOA is estimated in the first place, then a Maximum-Likelihood (ML) estimation based on peak search is applied to a two-dimensional grids providing estimation of initial velocity and acceleration. Simulations show that the MIMO radar has a better performance in DOA estimation than the phased array radar. By means of Monte Carlo simulations, the estimation error of initial velocity and acceleration on different SNRs are calculated. The results also suggest the effectiveness of this method.展开更多
基金Supported by the program for the Fundamental Research Funds for the Central Universities(2014RC042,2015JBM109)
文摘In this article, we consider a lifetime distribution, the Weibull-Logarithmic distri- bution introduced by [6]. We investigate some new statistical characterizations and properties. We develop the maximum likelihood inference using EM algorithm. Asymptotic properties of the MLEs are obtained and extensive simulations are conducted to assess the performance of parameter estimation. A numerical example is used to illustrate the application.
基金Supported by the National Science Foundation of China(11901236,12261036)Scientific Research Fund of Hunan Provincial Education Department(21A0328)+2 种基金Provincial Natural Science Foundation of Hunan(2022JJ30469)Young Core Teacher Foundation of Hunan Province([2020]43)Provincial Postgraduate Innovation Foundation of Hunan(CX20221113)。
文摘Weighted exponential distribution W ED(α,λ)with shape parameterαand scale parameterλpossesses some good properties and can be used as a good fit to survival time data compared to other distributions such as gamma,Weibull,or generalized exponential distribution.In this article,we proved the existence and uniqueness of the maximum likelihood estimator(MLE)of the parameters of W ED(α,λ)in simple random sampling(SRS)and provided explicit expressions for the Fisher information number in SRS.Moreover,we also proved the existence and uniqueness of the MLE of the parameters of W ED(α,λ)in ranked set sampling(RSS)and provided explicit expressions for the Fisher information number in RSS.Simulation studies show that these MLEs in RSS can be real competitors for those in SRS.
基金supported in part by the National Key Research and Development Program of China(2023YFB3906403)the National Natural Science Foundation of China(62373118,62173105)the Natural Science Foundation of Heilongjiang Province of China(ZD2023F002)
文摘Over the past few decades, numerous adaptive Kalman filters(AKFs) have been proposed. However, achieving online estimation with both high estimation accuracy and fast convergence speed is challenging, especially when both the process noise and measurement noise covariance matrices are relatively inaccurate. Maximum likelihood estimation(MLE) possesses the potential to achieve this goal, since its theoretical accuracy is guaranteed by asymptotic optimality and the convergence speed is fast due to weak dependence on accurate state estimation.Unfortunately, the maximum likelihood cost function is so intricate that the existing MLE methods can only simply ignore all historical measurement information to achieve online estimation,which cannot adequately realize the potential of MLE. In order to design online MLE-based AKFs with high estimation accuracy and fast convergence speed, an online exploratory MLE approach is proposed, based on which a mini-batch coordinate descent noise covariance matrix estimation framework is developed. In this framework, the maximum likelihood cost function is simplified for online estimation with fewer and simpler terms which are selected in a mini-batch and calculated with a backtracking method. This maximum likelihood cost function is sidestepped and solved by exploring possible estimated noise covariance matrices adaptively while the historical measurement information is adequately utilized. Furthermore, four specific algorithms are derived under this framework to meet different practical requirements in terms of convergence speed, estimation accuracy,and calculation load. Abundant simulations and experiments are carried out to verify the validity and superiority of the proposed algorithms as compared with existing state-of-the-art AKFs.
文摘A Bayesian approach using Markov chain Monte Carlo algorithms has been developed to analyze Smith’s discretized version of the discovery process model. It avoids the problems involved in the maximum likelihood method by effectively making use of the information from the prior distribution and that from the discovery sequence according to posterior probabilities. All statistical inferences about the parameters of the model and total resources can be quantified by drawing samples directly from the joint posterior distribution. In addition, statistical errors of the samples can be easily assessed and the convergence properties can be monitored during the sampling. Because the information contained in a discovery sequence is not enough to estimate all parameters, especially the number of fields, geologically justified prior information is crucial to the estimation. The Bayesian approach allows the analyst to specify his subjective estimates of the required parameters and his degree of uncertainty about the estimates in a clearly identified fashion throughout the analysis. As an example, this approach is applied to the same data of the North Sea on which Smith demonstrated his maximum likelihood method. For this case, the Bayesian approach has really improved the overly pessimistic results and downward bias of the maximum likelihood procedure.
基金Undergraduate Education High land Construction Project of Shanghaithe Key Course Construction of Shanghai Education Committee (No.20075302)the Key Technology R&D Program of Shanghai Municipality (No.08160510600)
文摘In order to obtain the life information of the vacuum fluorescent display （VFD） in a short time, a model of constant stress accelerated life tests （CSALT） is established with its filament temperature increased, and four constant stress tests are conducted. The Weibull function is applied to describe the life distribution of the VFD, and the maximum likelihood estimation （MLE） and its iterative flow chart are used to calculate the shape parameters and the scale parameters. Furthermore, the accelerated life equation is determined by the least square method, the Kolmogorov-Smirnov test is performed to verify whether the VFD life meets the Weibull distribution or not, and selfdeveloped software is employed to predict the average life and the reliable life. Statistical data analysis results demonstrate that the test plans are feasible and versatile, that the VFD life follows the Weibull distribution, and that the VFD accelerated model satisfies the linear Arrhenius equation. The proposed method and the estimated life information of the VFD can provide some significant guideline to its manufacturers and customers.
文摘随着风电渗透率的持续上升,电力系统的惯量水平显著下降,对系统频率稳定性构成了新的挑战。为有效评估风电并网情况下电力系统节点惯量的变化,提出了一种基于受控自回归滑动平均(autoregressive moving average with exogenous variable,ARMAX)模型的改进最大似然估计(maximum likelihood estimation,MLE)参数辨识方法对系统机组直接相连节点进行惯量评估。首先,构建ARMAX模型对发电机组直接相连节点的动态特性进行建模,并利用改进MLE对模型参数进行辨识,以评估与机组直接相连的节点惯量。然后,基于k-means聚类算法对发电机组节点惯量进行分区,计算得到系统区域惯量和中心频率,并进一步对非发电机组节点频率进行自适应多项式拟合计算,得到其系统节点惯量。最后,搭建IEEE39含风力发电机组节点系统,绘制热力图直观展示电力系统节点和区域的惯量分布,验证了所提改进方法的有效性。该方法有助于精准识别系统中不同节点的动态响应特性,为风电并网系统的分析和规划提供了有力支持。
基金The National Natural Science Foundation of China(No.11171065)the Natural Science Foundation of Jiangsu Province(No.BK2011058)
文摘In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.
基金supported by Joint Foundation of and China Academy of Engineering Physical(10676006)
文摘To estimate the spreading sequence of the direct sequence spread spectrum(DSSS)signal,a fast algorithm based on maximum likelihood function is proposed,and the theoretical derivation of the algorithm is provided.By simplifying the objective function of maximum likelihood estimation,the algorithm can realize sequence synchronization and sequence estimation via adaptive iteration and sliding window.Since it avoids the correlation matrix computation,the algorithm significantly reduces the storage requirement and the computation complexity.Simulations show that it is a fast convergent algorithm,and can perform well in low signal to noise ratio(SNR).
基金supported by the National Science Foundations (DMS0504783 DMS0604207)National Science Fund for Distinguished Young Scholars of China (70825005)
文摘This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.
文摘A crowdsourcing experiment in which viewers (the “crowd”) of a British Broadcasting Corporation (BBC) television show submitted estimates of the number of coins in a tumbler was shown in an antecedent paper (Part 1) to follow a log-normal distribution ∧(m,s2). The coin-estimation experiment is an archetype of a broad class of image analysis and object counting problems suitable for solution by crowdsourcing. The objective of the current paper (Part 2) is to determine the location and scale parameters (m,s) of ∧(m,s2) by both Bayesian and maximum likelihood (ML) methods and to compare the results. One outcome of the analysis is the resolution, by means of Jeffreys’ rule, of questions regarding the appropriate Bayesian prior. It is shown that Bayesian and ML analyses lead to the same expression for the location parameter, but different expressions for the scale parameter, which become identical in the limit of an infinite sample size. A second outcome of the analysis concerns use of the sample mean as the measure of information of the crowd in applications where the distribution of responses is not sought or known. In the coin-estimation experiment, the sample mean was found to differ widely from the mean number of coins calculated from ∧(m,s2). This discordance raises critical questions concerning whether, and under what conditions, the sample mean provides a reliable measure of the information of the crowd. This paper resolves that problem by use of the principle of maximum entropy (PME). The PME yields a set of equations for finding the most probable distribution consistent with given prior information and only that information. If there is no solution to the PME equations for a specified sample mean and sample variance, then the sample mean is an unreliable statistic, since no measure can be assigned to its uncertainty. Parts 1 and 2 together demonstrate that the information content of crowdsourcing resides in the distribution of responses (very often log-normal in form), which can be obtained empirically or by appropriate modeling.
基金supported by the National Natural Science Foundation of China (No. 61002026)
文摘To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, thus its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an appropriate grid spacing adaptively, and is able to yield approximate maximum likelihood estimate （MLE） with a computational complexity of O（n2）. Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing methods. Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate similarly by grid search.
文摘By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of the identification parameters is given. In order to decrease the asymptotic error, a corrector of maximum likelihood (CML) estimation with its recursive algorithm is given. It has been proved that the corrector has smaller asymptotic error than the least square methods. A simulation example shows that the corrector of maximum likelihood estimation is of higher approximating precision to the true parameters than the least square methods.
文摘In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression model with exact linear restrictions. However, there are some situations, where the linear restrictions are stochastic. In this paper, we propose a Stochastic Restricted Maximum Likelihood Estimator (SRMLE) for the logistic regression model with stochastic linear restrictions to overcome this issue. Moreover, a Monte Carlo simulation is conducted for comparing the performances of the MLE, Restricted Maximum Likelihood Estimator (RMLE), Ridge Type Logistic Estimator(LRE), Liu Type Logistic Estimator(LLE), and SRMLE for the logistic regression model by using Scalar Mean Squared Error (SMSE).
文摘Maximum likelihood estimation(MLE)is an effective method for localizing radioactive sources in a given area.However,it requires an exhaustive search for parameter estimation,which is time-consuming.In this study,heuristic techniques were employed to search for radiation source parameters that provide the maximum likelihood by using a network of sensors.Hence,the time consumption of MLE would be effectively reduced.First,the radiation source was detected using the k-sigma method.Subsequently,the MLE was applied for parameter estimation using the readings and positions of the detectors that have detected the radiation source.A comparative study was performed in which the estimation accuracy and time consump-tion of the MLE were evaluated for traditional methods and heuristic techniques.The traditional MLE was performed via a grid search method using fixed and multiple resolutions.Additionally,four commonly used heuristic algorithms were applied:the firefly algorithm(FFA),particle swarm optimization(PSO),ant colony optimization(ACO),and artificial bee colony(ABC).The experiment was conducted using real data collected by the Low Scatter Irradiator facility at the Savannah River National Laboratory as part of the Intelligent Radiation Sensing System program.The comparative study showed that the estimation time was 3.27 s using fixed resolution MLE and 0.59 s using multi-resolution MLE.The time consumption for the heuristic-based MLE was 0.75,0.03,0.02,and 0.059 s for FFA,PSO,ACO,and ABC,respectively.The location estimation error was approximately 0.4 m using either the grid search-based MLE or the heuristic-based MLE.Hence,heuristic-based MLE can provide comparable estimation accuracy through a less time-consuming process than traditional MLE.
文摘In this paper a method of aerodynamic parameter identification of vehicle, the maximum likelihood method, is introduced. The aerodynamic model of vehicle is identified and the basic equations using maximum likelihood method are established. After that, the simulation data is identified to verify the correctness of the mathematic model and identification method. Last, the practical flight data is identified and analyzed.
基金supported by the Fund for Foreign Scholars in University Research and Teaching Programs(the 111 Project)(B18039).
文摘Low elevation estimation,which has attracted wide attention due to the presence of specular multipath,is essential for tracking radars.Frequency agility not only has the advantage of strong anti-interference ability,but also can enhance the performance of tracking radars.A frequency-agile refined maximum likelihood(RML)algorithm based on optimal fusion is proposed.The algorithm constructs an optimization problem,which minimizes the mean square error(MSE)of angle estimation.Thereby,the optimal weight at different frequency points is obtained for fusing the angle estimation.Through theoretical analysis and simulation,the frequency-agile RML algorithm based on optimal fusion can improve the accuracy of angle estimation effectively.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11574291,61108009 and 61222504
文摘As a widely used reconstruction algorithm in quantum state tomography, maximum likelihood estimation tends to assign a rank-deficient matrix, which decreases estimation accuracy for certain quantum states. Fortunately, hedged maximum likelihood estimation （HMLE） [Phys. Rev. Lett. 105 （2010）200504] was proposed to avoid this problem. Here we study more details about this proposal in the two-qubit case and further improve its performance. We ameliorate the HMLE method by updating the hedging function based on the purity of the estimated state. Both performances of HMLE and ameliorated HMLE are demonstrated by numerical simulation and experimental implementation on the Werner states of polarization-entangled photons.
基金the National Natural Science Foundation of China(62071144,61971159,61871149).
文摘The conformal array can make full use of the aperture,save space,meet the requirements of aerodynamics,and is sensitive to polarization information.It has broad application prospects in military,aerospace,and communication fields.The joint polarization and direction-of-arrival(DOA)estimation based on the conformal array and the theoretical analysis of its parameter estimation performance are the key factors to promote the engineering application of the conformal array.To solve these problems,this paper establishes the wave field signal model of the conformal array.Then,for the case of a single target,the cost function of the maximum likelihood(ML)estimator is rewritten with Rayleigh quotient from a problem of maximizing the ratio of quadratic forms into those of minimizing quadratic forms.On this basis,rapid parameter estimation is achieved with the idea of manifold separation technology(MST).Compared with the modified variable projection(MVP)algorithm,it reduces the computational complexity and improves the parameter estimation performance.Meanwhile,the MST is used to solve the partial derivative of the steering vector.Then,the theoretical performance of ML,the multiple signal classification(MUSIC)estimator and Cramer-Rao bound(CRB)based on the conformal array are derived respectively,which provides theoretical foundation for the engineering application of the conformal array.Finally,the simulation experiment verifies the effectiveness of the proposed method.
文摘The estimation of target parameters in MIMO radar signal processing is one of the most important research topics. An efficient implementation of the Maximum Likelihood estimator is presented in this paper to estimate the DOA (Direction of Arrival), initial velocity and acceleration of a maneuvering target in colocated MIMO radar. The target’s DOA is estimated in the first place, then a Maximum-Likelihood (ML) estimation based on peak search is applied to a two-dimensional grids providing estimation of initial velocity and acceleration. Simulations show that the MIMO radar has a better performance in DOA estimation than the phased array radar. By means of Monte Carlo simulations, the estimation error of initial velocity and acceleration on different SNRs are calculated. The results also suggest the effectiveness of this method.
