The estimation of the probability of informed trading(PIN)model and its extensions poses significant challenges owing to various computational problems.To address these issues,we propose a novel estimation method call...The estimation of the probability of informed trading(PIN)model and its extensions poses significant challenges owing to various computational problems.To address these issues,we propose a novel estimation method called the expectation-conditional-maximization(ECM)algorithm,which can serve as an alternative to the existing methods for estimating PIN models.Our method provides optimal estimates for the original PIN model as well as two of its extensions:the multilayer PIN model and the adjusted PIN model,along with its restricted versions.Our results indicate that estimations using the ECM algorithm are generally faster,more accurate,and more memory-efficient than the standard methods used in the literature,making it a robust alternative.More importantly,the ECM algorithm is not limited to the models discussed and can be easily adapted to estimate future extensions of the PIN model.展开更多
In this paper, a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for two-point boundary value problems. The key idea is to postprocess the Galerkin approximation, and the analysis sh...In this paper, a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for two-point boundary value problems. The key idea is to postprocess the Galerkin approximation, and the analysis shows that the postproeess improves the order of convergence. Consequently, we obtain asymptotically exact aposteriori error estimators based on the postprocessing results. Numerical examples are included to illustrate the theoretical analysis.展开更多
One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies de- grees of freedom. As far as safety questions are concerned knowledge about the error introduced by the r...One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies de- grees of freedom. As far as safety questions are concerned knowledge about the error introduced by the reduction of the flexible degrees of freedom is helpful and very important. In this work, an a-posteriori error estimator for linear first order systems is extended for error estimation of me- chanical second order systems. Due to the special second order structure of mechanical systems, an improvement of the a-posteriori error estimator is achieved. A major advan- tage of the a-posteriori error estimator is that the estimator is independent of the used reduction technique. Therefore, it can be used for moment-matching based, Gramian matrices based or modal based model reduction techniques. The capability of the proposed technique is demon- strated by the a-posteriori error estimation of a mechanical system, and a sensitivity analysis of the parameters involved in the error estimation process is conducted.展开更多
This paper considers the Bayesian and expected Bayesian（E-Bayesian） estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censori...This paper considers the Bayesian and expected Bayesian（E-Bayesian） estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censoring scheme（PHCS）. The estimations are obtained based on Gamma conjugate prior for the parameter under squared error（SE） and Linex loss functions. The simulation results are provided for the comparison purpose and one data set is analyzed.展开更多
Aiming at the problems of low measurement accuracy,uncertainty and nonlinearity of random noise of the micro electro mechanical system(MEMS)gyroscope,a gyroscope noise estimation and filtering method is proposed,which...Aiming at the problems of low measurement accuracy,uncertainty and nonlinearity of random noise of the micro electro mechanical system(MEMS)gyroscope,a gyroscope noise estimation and filtering method is proposed,which combines expectation maximum(EM)with maximum a posterior(MAP)to form an adpative unscented Kalman filter(UKF),called EMMAP-UKF.According to the MAP estimation principle,a suboptimal unbiased MAP noise statistical estimation model is constructed.Then,EM algorithm is introduced to transform the noise estimation problem into the mathematical expectation maximization problem,which can dynamically adjust the variance of the observed noise.Finally,the estimation and filtering of gyroscope random drift error can be realized.The performance of the gyro noise filtering method is evaluated by Allan variance,and the effectiveness of the method is verified by hardware-in-the-loop simulation.展开更多
In dynamic environments, the moving landmarks can make the accuracy of traditional vision-based pose estimation worse or even failure. To solve this problem, a robust Gaussian mixture model for vision-based pose estim...In dynamic environments, the moving landmarks can make the accuracy of traditional vision-based pose estimation worse or even failure. To solve this problem, a robust Gaussian mixture model for vision-based pose estimation is proposed. The motion index is added to the traditional graph-based vision-based pose estimation model to describe landmarks’ moving probability, transforming the classic Gaussian model to Gaussian mixture model, which can reduce the influence of moving landmarks for optimization results. To improve the algorithm’s robustness to noise, the covariance inflation model is employed in residual equations. The expectation maximization method for solving the Gaussian mixture problem is derived in detail, transforming the problem into classic iterative least square problem. Experimental results demonstrate that in dynamic environments, the proposed method outperforms the traditional method both in absolute accuracy and relative accuracy, while maintains high accuracy in static environments. The proposed method can effectively reduce the influence of the moving landmarks in dynamic environments, which is more suitable for the autonomous localization of mobile robots.展开更多
A channel estimation approach for orthogonal frequency division multiplexing with multiple-input and multipleoutput （MIMO-OFDM） in rapid fading channels is proposed. This approach combines the advantages of an optim...A channel estimation approach for orthogonal frequency division multiplexing with multiple-input and multipleoutput （MIMO-OFDM） in rapid fading channels is proposed. This approach combines the advantages of an optimal training sequence based least-square （OLS） algorithm and an expectation-maximization （EM） algorithm. The channels at the training blocks are estimated using an estimator based on the OLS algorithm. To compensate for the fast Rayleigh fading at the data blocks, a time domain based Gaussian interpolation filter is presented. Furthermore, an EM algorithm is introduced to improve the performance of channel estimation by a few iterations. Simulations show that this channel estimation approach can effectively track rapid channel variation.展开更多
A new method in making judgment matrix is proposed based on a basic value of “importance” and a relative measure level of “importance”. Factors affecting petroleum exploration are analyzed and Experts’ judgment m...A new method in making judgment matrix is proposed based on a basic value of “importance” and a relative measure level of “importance”. Factors affecting petroleum exploration are analyzed and Experts’ judgment matrix on a geologic formation is given. Expected value of each factor is computed and the volume of recoverable oil is estimated.展开更多
An enhanced expectation maximization （ with channel time variation is proposed for mobile EM） based iterative channel estimator for coping multiple input multi output orthogonal frequency division multiplexing （MIM...An enhanced expectation maximization （ with channel time variation is proposed for mobile EM） based iterative channel estimator for coping multiple input multi output orthogonal frequency division multiplexing （MIMO OFDM） systems. In the proposed scheme, the recursive least squares （RLS） algorithm is applied to track the time varying channel impulse response （CIR） within several symbols. By using the tracked time varying CIR, the ICI are constructed and then cancelled from the received signal, thus reducing their impactions on the channel estimation. Moreover, based on an o ver sampled complex exponential basis expansion model （ OCE BEM）, an improved channel predic tor is derived in order to improve the initial channel estimates accuracy of the iterative estimator. Simulation results show that ying scenarios with a smaller the proposed scheme outperforms the classic counterpart in time var cost of complexity.展开更多
Sample size re-estimation is essential in oncology studies. However, the use of blinded sample size reassessment for survival data has been rarely reported. Based on the density function of the exponential distributio...Sample size re-estimation is essential in oncology studies. However, the use of blinded sample size reassessment for survival data has been rarely reported. Based on the density function of the exponential distribution, an expectation-maximization（EM） algorithm of the hazard ratio was derived, and several simulation studies were used to verify its applications. The method had obvious variation in the hazard ratio estimates and overestimation for the relatively small hazard ratios. Our studies showed that the stability of the EM estimation results directly correlated with the sample size, the convergence of the EM algorithm was impacted by the initial values, and a balanced design produced the best estimates. No reliable blinded sample size re-estimation inference can be made in our studies, but the results provide useful information to steer the practitioners in this field from repeating the same endeavor.展开更多
In this work, for a control consumption-investment process with the discounted reward optimization criteria, a numerical estimate of the stability index is made. Using explicit formulas for the optimal stationary poli...In this work, for a control consumption-investment process with the discounted reward optimization criteria, a numerical estimate of the stability index is made. Using explicit formulas for the optimal stationary policies and for the value functions, the stability index is explicitly calculated and through statistical techniques its asymptotic behavior is investigated (using numerical experiments) when the discount coefficient approaches 1. The results obtained define the conditions under which an approximate optimal stationary policy can be used to control the original process.展开更多
In statistical theory, a statistic that is function of sample observations is used to estimate distribution parameter. This statistic is called unbiased estimate if its expectation is equal to theoretical parameter. P...In statistical theory, a statistic that is function of sample observations is used to estimate distribution parameter. This statistic is called unbiased estimate if its expectation is equal to theoretical parameter. Proving whether or not a statistic is unbiased estimate is very important but this proof may require a lot of efforts when statistic is complicated function. Therefore, this research facilitates this proof by proposing a theorem which states that the expectation of variable x 〉 0 is u if and only if the limit of logarithm expectation of x approaches logarithm of u. In order to make clear of this theorem, the research gives an example of proving correlation coefficient as unbiased estimate by taking advantages of this theorem.展开更多
The simplified joint channel estimation and symbol detection based on the EM (expectation-maximization) algorithm for space-time block code (STBC) are proposed. By assuming channel to be invariant within only one STBC...The simplified joint channel estimation and symbol detection based on the EM (expectation-maximization) algorithm for space-time block code (STBC) are proposed. By assuming channel to be invariant within only one STBC word and utilizing the orthogonal structure of STBC, the computational complexity and cost of this algorithm are both very low, so it is very suitable to implementation in real systems.展开更多
This paper proposes a method for obtaining nonlinear models of distribution grid based on available measurements from the power grid.We formulate a maximum likelihood estimation(MLE)problem that estimates unknown line...This paper proposes a method for obtaining nonlinear models of distribution grid based on available measurements from the power grid.We formulate a maximum likelihood estimation(MLE)problem that estimates unknown line parameters—specifically,the impedance between nodes—using measured voltage magnitudes and net active and reactive power injections at each node.The nonlinear model for the distribution grid uses a nonlinear approximation of the DistFlow model,which includes line losses and is parameterized by the unknown line impedances.We solve the resulting MLE problem using an expectation maximization(EM)algorithm,tailored for the nonlinear model,and provide a numerically robust implementation.The proposed method is demonstrated on the IEEE 37-node test network,and we compare it with the state-of-the-art methods.The proposed method achieves a 70%reduction in voltage error and an error for state variables that is more than 10000 times smaller.A final comparison uses data from a real network,and the proposed method achieves parameter estimates with errors 100 times smaller than competing methods.展开更多
Sideslip angle,yaw rate,and vehicle velocity are essential for intelligent vehicle control.Since these vehicle states are not measured directly,some Kalman-based approaches have been developed to estimate these states...Sideslip angle,yaw rate,and vehicle velocity are essential for intelligent vehicle control.Since these vehicle states are not measured directly,some Kalman-based approaches have been developed to estimate these states using in-vehicle sensors.However,the existing studies seldom account for the influence of sensor data loss on estimation accuracy.In addition,the process and measurement noise change during the estimation process because of the various driving conditions.To address these problems,an expectation-maximization robust extended Kalman filter(EMREKF)is proposed.Firstly,a robust extended Kalman filter(REKF)is developed to deal with the impact of missing measurements.Then,an improved expectation maximization(EM)algorithm that considers data loss is presented to update the noise parameter of the REKF dynamically.Finally,the improved EM is fused with the REKF to form the EMREKF to estimate vehicle state.The experimental results demonstrate that the EMREKF outperforms EKF,REKF,and maximum correntropy criterion EKF for various degrees of data loss and the proposed algorithm has a strong adaptive ability to different driving conditions.展开更多
H-infinity estimator is generally implemented in timevariant state-space models, but it leads to high complexity when the model is used for multiple input multiple output with orthogo- hal frequency division multiplex...H-infinity estimator is generally implemented in timevariant state-space models, but it leads to high complexity when the model is used for multiple input multiple output with orthogo- hal frequency division multiplexing （MIMO-OFDM） systems. Thus, an H-infinity estimator over time-invariant system models is pro- posed, which modifies the Krein space accordingly. In order to avoid the large matrix inversion and multiplication required in each OFDM symbol from different transmit antennas, expectation maximization （EM） is developed to reduce the high computational load. Joint estimation over multiple OFDM symbols is used to resist the high pilot overhead generated by the increasing number of transmit antennas. Finally, the performance of the proposed estimator is enhanced via an angle-domain process. Through performance analysis and simulation experiments, it is indicated that the pro- posed algorithm has a better mean square error （MSE） and bit error rate （BER） performance than the optimal least square （LS） estimator. Joint estimation over multiple OFDM symbols can not only reduce the pilot overhead but also promote the channel performance. What is more, an obvious improvement can be obtained by using the angle-domain filter.展开更多
A higher order finite element method is considered to treat an interface problem. The polynomial degree is allowed to be arbitrary but it is fixed for the FEM-variational formulation. We propose an error estimator whi...A higher order finite element method is considered to treat an interface problem. The polynomial degree is allowed to be arbitrary but it is fixed for the FEM-variational formulation. We propose an error estimator which turns out to be efficient and reliable. We demonstrate upper and lower bounds of the error estimator with respect to the exact accuracy. For the transmission problem, the coefficients for the internal and external domains can be highly dissimilar. One major difficulty is the characteristic of the estimator at the interface. The a-posteriori error estimates can be computed very efficiently element by element. To corroborate the theoretical analysis, we report on a few numerical results.展开更多
In this paper,we investigate some asymptotic properties of the least squares estimator in nonlinear regression model with independent and identically distributed random errors under sub-linear expectations.The large d...In this paper,we investigate some asymptotic properties of the least squares estimator in nonlinear regression model with independent and identically distributed random errors under sub-linear expectations.The large deviation results for the estimator are established under some general conditions.As applications,the results on weak consistency and strong consistency are obtained under the meaning of capacity.A simulation study is also presented to verify the validity of the theoretical results.展开更多
基金supported by the Scientific and Technological Research Council of Turkey(TUBITAK)[grant no 122K637].
文摘The estimation of the probability of informed trading(PIN)model and its extensions poses significant challenges owing to various computational problems.To address these issues,we propose a novel estimation method called the expectation-conditional-maximization(ECM)algorithm,which can serve as an alternative to the existing methods for estimating PIN models.Our method provides optimal estimates for the original PIN model as well as two of its extensions:the multilayer PIN model and the adjusted PIN model,along with its restricted versions.Our results indicate that estimations using the ECM algorithm are generally faster,more accurate,and more memory-efficient than the standard methods used in the literature,making it a robust alternative.More importantly,the ECM algorithm is not limited to the models discussed and can be easily adapted to estimate future extensions of the PIN model.
基金supported partially by the innovation fund of Shanghai Normal Universitysupported partially by NSERC of Canada under Grant OGP0046726.
文摘In this paper, a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for two-point boundary value problems. The key idea is to postprocess the Galerkin approximation, and the analysis shows that the postproeess improves the order of convergence. Consequently, we obtain asymptotically exact aposteriori error estimators based on the postprocessing results. Numerical examples are included to illustrate the theoretical analysis.
文摘One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies de- grees of freedom. As far as safety questions are concerned knowledge about the error introduced by the reduction of the flexible degrees of freedom is helpful and very important. In this work, an a-posteriori error estimator for linear first order systems is extended for error estimation of me- chanical second order systems. Due to the special second order structure of mechanical systems, an improvement of the a-posteriori error estimator is achieved. A major advan- tage of the a-posteriori error estimator is that the estimator is independent of the used reduction technique. Therefore, it can be used for moment-matching based, Gramian matrices based or modal based model reduction techniques. The capability of the proposed technique is demon- strated by the a-posteriori error estimation of a mechanical system, and a sensitivity analysis of the parameters involved in the error estimation process is conducted.
基金supported by the National Natural Science Foundation of China(7117116471401134+1 种基金71571144)the Natural Science Basic Research Program of Shaanxi Province(2015JM1003)
文摘This paper considers the Bayesian and expected Bayesian（E-Bayesian） estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censoring scheme（PHCS）. The estimations are obtained based on Gamma conjugate prior for the parameter under squared error（SE） and Linex loss functions. The simulation results are provided for the comparison purpose and one data set is analyzed.
基金National Natural Science Foundation of China(No.61863024)Scientific Research Projects of Higher Institutions of Gansu Province(No.2018C-11)+1 种基金Natural Science Foundation of Gansu Province(No.18JR3RA107)Science and Technology Program of Gansu Province(No.18CX3ZA004)。
文摘Aiming at the problems of low measurement accuracy,uncertainty and nonlinearity of random noise of the micro electro mechanical system(MEMS)gyroscope,a gyroscope noise estimation and filtering method is proposed,which combines expectation maximum(EM)with maximum a posterior(MAP)to form an adpative unscented Kalman filter(UKF),called EMMAP-UKF.According to the MAP estimation principle,a suboptimal unbiased MAP noise statistical estimation model is constructed.Then,EM algorithm is introduced to transform the noise estimation problem into the mathematical expectation maximization problem,which can dynamically adjust the variance of the observed noise.Finally,the estimation and filtering of gyroscope random drift error can be realized.The performance of the gyro noise filtering method is evaluated by Allan variance,and the effectiveness of the method is verified by hardware-in-the-loop simulation.
文摘In dynamic environments, the moving landmarks can make the accuracy of traditional vision-based pose estimation worse or even failure. To solve this problem, a robust Gaussian mixture model for vision-based pose estimation is proposed. The motion index is added to the traditional graph-based vision-based pose estimation model to describe landmarks’ moving probability, transforming the classic Gaussian model to Gaussian mixture model, which can reduce the influence of moving landmarks for optimization results. To improve the algorithm’s robustness to noise, the covariance inflation model is employed in residual equations. The expectation maximization method for solving the Gaussian mixture problem is derived in detail, transforming the problem into classic iterative least square problem. Experimental results demonstrate that in dynamic environments, the proposed method outperforms the traditional method both in absolute accuracy and relative accuracy, while maintains high accuracy in static environments. The proposed method can effectively reduce the influence of the moving landmarks in dynamic environments, which is more suitable for the autonomous localization of mobile robots.
基金Project supported by the National High-Technology Research and Development Program of China （Grant No. 2003AA123- 31007）, and the National Natural Science Foundation of China （Grant No.60272079）
文摘A channel estimation approach for orthogonal frequency division multiplexing with multiple-input and multipleoutput （MIMO-OFDM） in rapid fading channels is proposed. This approach combines the advantages of an optimal training sequence based least-square （OLS） algorithm and an expectation-maximization （EM） algorithm. The channels at the training blocks are estimated using an estimator based on the OLS algorithm. To compensate for the fast Rayleigh fading at the data blocks, a time domain based Gaussian interpolation filter is presented. Furthermore, an EM algorithm is introduced to improve the performance of channel estimation by a few iterations. Simulations show that this channel estimation approach can effectively track rapid channel variation.
文摘A new method in making judgment matrix is proposed based on a basic value of “importance” and a relative measure level of “importance”. Factors affecting petroleum exploration are analyzed and Experts’ judgment matrix on a geologic formation is given. Expected value of each factor is computed and the volume of recoverable oil is estimated.
基金Supported by the National Natural Science Foundation of China(6096200161071088)
文摘An enhanced expectation maximization （ with channel time variation is proposed for mobile EM） based iterative channel estimator for coping multiple input multi output orthogonal frequency division multiplexing （MIMO OFDM） systems. In the proposed scheme, the recursive least squares （RLS） algorithm is applied to track the time varying channel impulse response （CIR） within several symbols. By using the tracked time varying CIR, the ICI are constructed and then cancelled from the received signal, thus reducing their impactions on the channel estimation. Moreover, based on an o ver sampled complex exponential basis expansion model （ OCE BEM）, an improved channel predic tor is derived in order to improve the initial channel estimates accuracy of the iterative estimator. Simulation results show that ying scenarios with a smaller the proposed scheme outperforms the classic counterpart in time var cost of complexity.
基金supported by the National Natural Science Foundation of China(81273184)the National Natural Science Foundation of China Grant for Young Scientists (81302512)
文摘Sample size re-estimation is essential in oncology studies. However, the use of blinded sample size reassessment for survival data has been rarely reported. Based on the density function of the exponential distribution, an expectation-maximization（EM） algorithm of the hazard ratio was derived, and several simulation studies were used to verify its applications. The method had obvious variation in the hazard ratio estimates and overestimation for the relatively small hazard ratios. Our studies showed that the stability of the EM estimation results directly correlated with the sample size, the convergence of the EM algorithm was impacted by the initial values, and a balanced design produced the best estimates. No reliable blinded sample size re-estimation inference can be made in our studies, but the results provide useful information to steer the practitioners in this field from repeating the same endeavor.
文摘In this work, for a control consumption-investment process with the discounted reward optimization criteria, a numerical estimate of the stability index is made. Using explicit formulas for the optimal stationary policies and for the value functions, the stability index is explicitly calculated and through statistical techniques its asymptotic behavior is investigated (using numerical experiments) when the discount coefficient approaches 1. The results obtained define the conditions under which an approximate optimal stationary policy can be used to control the original process.
文摘In statistical theory, a statistic that is function of sample observations is used to estimate distribution parameter. This statistic is called unbiased estimate if its expectation is equal to theoretical parameter. Proving whether or not a statistic is unbiased estimate is very important but this proof may require a lot of efforts when statistic is complicated function. Therefore, this research facilitates this proof by proposing a theorem which states that the expectation of variable x 〉 0 is u if and only if the limit of logarithm expectation of x approaches logarithm of u. In order to make clear of this theorem, the research gives an example of proving correlation coefficient as unbiased estimate by taking advantages of this theorem.
基金This project was supported by the National Natural Science Foundation of China (60272079).
文摘The simplified joint channel estimation and symbol detection based on the EM (expectation-maximization) algorithm for space-time block code (STBC) are proposed. By assuming channel to be invariant within only one STBC word and utilizing the orthogonal structure of STBC, the computational complexity and cost of this algorithm are both very low, so it is very suitable to implementation in real systems.
文摘This paper proposes a method for obtaining nonlinear models of distribution grid based on available measurements from the power grid.We formulate a maximum likelihood estimation(MLE)problem that estimates unknown line parameters—specifically,the impedance between nodes—using measured voltage magnitudes and net active and reactive power injections at each node.The nonlinear model for the distribution grid uses a nonlinear approximation of the DistFlow model,which includes line losses and is parameterized by the unknown line impedances.We solve the resulting MLE problem using an expectation maximization(EM)algorithm,tailored for the nonlinear model,and provide a numerically robust implementation.The proposed method is demonstrated on the IEEE 37-node test network,and we compare it with the state-of-the-art methods.The proposed method achieves a 70%reduction in voltage error and an error for state variables that is more than 10000 times smaller.A final comparison uses data from a real network,and the proposed method achieves parameter estimates with errors 100 times smaller than competing methods.
基金supported by the National Natural Science Foundation of China(Grant No.52402482).
文摘Sideslip angle,yaw rate,and vehicle velocity are essential for intelligent vehicle control.Since these vehicle states are not measured directly,some Kalman-based approaches have been developed to estimate these states using in-vehicle sensors.However,the existing studies seldom account for the influence of sensor data loss on estimation accuracy.In addition,the process and measurement noise change during the estimation process because of the various driving conditions.To address these problems,an expectation-maximization robust extended Kalman filter(EMREKF)is proposed.Firstly,a robust extended Kalman filter(REKF)is developed to deal with the impact of missing measurements.Then,an improved expectation maximization(EM)algorithm that considers data loss is presented to update the noise parameter of the REKF dynamically.Finally,the improved EM is fused with the REKF to form the EMREKF to estimate vehicle state.The experimental results demonstrate that the EMREKF outperforms EKF,REKF,and maximum correntropy criterion EKF for various degrees of data loss and the proposed algorithm has a strong adaptive ability to different driving conditions.
基金supported by the National Natural Science Foundation of China(6087410860904035+2 种基金61004052)the Directive Plan of Science Research from the Bureau of Education of Hebei Province(Z2009105)the Funds of Central Colleges Basic Scientific Operating Expense(N100604004)
文摘H-infinity estimator is generally implemented in timevariant state-space models, but it leads to high complexity when the model is used for multiple input multiple output with orthogo- hal frequency division multiplexing （MIMO-OFDM） systems. Thus, an H-infinity estimator over time-invariant system models is pro- posed, which modifies the Krein space accordingly. In order to avoid the large matrix inversion and multiplication required in each OFDM symbol from different transmit antennas, expectation maximization （EM） is developed to reduce the high computational load. Joint estimation over multiple OFDM symbols is used to resist the high pilot overhead generated by the increasing number of transmit antennas. Finally, the performance of the proposed estimator is enhanced via an angle-domain process. Through performance analysis and simulation experiments, it is indicated that the pro- posed algorithm has a better mean square error （MSE） and bit error rate （BER） performance than the optimal least square （LS） estimator. Joint estimation over multiple OFDM symbols can not only reduce the pilot overhead but also promote the channel performance. What is more, an obvious improvement can be obtained by using the angle-domain filter.
文摘A higher order finite element method is considered to treat an interface problem. The polynomial degree is allowed to be arbitrary but it is fixed for the FEM-variational formulation. We propose an error estimator which turns out to be efficient and reliable. We demonstrate upper and lower bounds of the error estimator with respect to the exact accuracy. For the transmission problem, the coefficients for the internal and external domains can be highly dissimilar. One major difficulty is the characteristic of the estimator at the interface. The a-posteriori error estimates can be computed very efficiently element by element. To corroborate the theoretical analysis, we report on a few numerical results.
基金supported by the National Natural Science Foundation of China(No.12471248)supported by grants from National Key R&D Program of China(No.2024YFA1013502)+1 种基金NSF of China(Grant No.U23A2064)the Summit Advancement Disciplines of Zhejiang Province(Zhejiang Gongshang University-Statistics)。
文摘In this paper,we investigate some asymptotic properties of the least squares estimator in nonlinear regression model with independent and identically distributed random errors under sub-linear expectations.The large deviation results for the estimator are established under some general conditions.As applications,the results on weak consistency and strong consistency are obtained under the meaning of capacity.A simulation study is also presented to verify the validity of the theoretical results.
