In order to improve the performance of the probability hypothesis density(PHD) algorithm based particle filter(PF) in terms of number estimation and states extraction of multiple targets, a new probability hypothesis ...In order to improve the performance of the probability hypothesis density(PHD) algorithm based particle filter(PF) in terms of number estimation and states extraction of multiple targets, a new probability hypothesis density filter algorithm based on marginalized particle and kernel density estimation is proposed, which utilizes the idea of marginalized particle filter to enhance the estimating performance of the PHD. The state variables are decomposed into linear and non-linear parts. The particle filter is adopted to predict and estimate the nonlinear states of multi-target after dimensionality reduction, while the Kalman filter is applied to estimate the linear parts under linear Gaussian condition. Embedding the information of the linear states into the estimated nonlinear states helps to reduce the estimating variance and improve the accuracy of target number estimation. The meanshift kernel density estimation, being of the inherent nature of searching peak value via an adaptive gradient ascent iteration, is introduced to cluster particles and extract target states, which is independent of the target number and can converge to the local peak position of the PHD distribution while avoiding the errors due to the inaccuracy in modeling and parameters estimation. Experiments show that the proposed algorithm can obtain higher tracking accuracy when using fewer sampling particles and is of lower computational complexity compared with the PF-PHD.展开更多
A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error ...A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error of the estimator are studied.展开更多
Let (X,Y) be an R^d×R^1 valued random vector (X_1,Y_1),…, (X_n,Y_n) be a random sample drawn from (X,Y), and let E|Y|<∞. The regression function m(x)=E(Y|X=x) for x∈R^d is estimated by where, and h_n is a p...Let (X,Y) be an R^d×R^1 valued random vector (X_1,Y_1),…, (X_n,Y_n) be a random sample drawn from (X,Y), and let E|Y|<∞. The regression function m(x)=E(Y|X=x) for x∈R^d is estimated by where, and h_n is a positive number depending upon n only, nad K is a given nonnegative function on R^d. In the paper, we study the L_p convergence rate of kernel estimate m_n(x) of m(x) in suitable condition, and improve and extend the results of Wei Lansheng.展开更多
Assume that f_(n)is the nonparametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional...Assume that f_(n)is the nonparametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere S^(d-1).We established that the large deviation principle for{sup_(x∈S^(d-1))|fn(x)-fn(-x)|,n≥1}holds if the kernel function is a function with bounded variation,and the density function f of the random variables is continuous and symmetric.展开更多
In the paper,we study the strong uniform consistency for the kernal estimates of random window w■th of density function and its derivatives under the condition that the sequence{X_n}of the ■ are the identically Φ-m...In the paper,we study the strong uniform consistency for the kernal estimates of random window w■th of density function and its derivatives under the condition that the sequence{X_n}of the ■ are the identically Φ-mixing random variabks.展开更多
There have been vast amount of studies on background modeling to detect moving objects. Two recent reviews[1,2] showed that kernel density estimation(KDE) method and Gaussian mixture model(GMM) perform about equally b...There have been vast amount of studies on background modeling to detect moving objects. Two recent reviews[1,2] showed that kernel density estimation(KDE) method and Gaussian mixture model(GMM) perform about equally best among possible background models. For KDE, the selection of kernel functions and their bandwidths greatly influence the performance. There were few attempts to compare the adequacy of functions for KDE. In this paper, we evaluate the performance of various functions for KDE. Functions tested include almost everyone cited in the literature and a new function, Laplacian of Gaussian(LoG) is also introduced for comparison. All tests were done on real videos with vary-ing background dynamics and results were analyzed both qualitatively and quantitatively. Effect of different bandwidths was also investigated.展开更多
Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we est...Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n).展开更多
In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness c...In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.展开更多
It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth o...It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation, which is completely based on data samples, is a long-term issue that has not been well settled so far. There exist analytic formulae of optimal kernel bandwidth, but they cannot be applied directly to data samples,since they depend on the unknown underlying density functions from which the samples are drawn. In this work, we devise an approach to pick out the totally data-based optimal bandwidth. First, we derive correction formulae for the analytic formulae of optimal bandwidth to compute the roughness of the sample's density function. Then substitute the correction formulae into the analytic formulae for optimal bandwidth, and through iteration we obtain the sample's optimal bandwidth. Compared with analytic formulae, our approach gives very good results, with relative differences from the analytic formulae being only 2%～3% for sample size larger than 10~4. This approach can also be generalized easily to cases of variable kernel estimations.展开更多
A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations o...A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.展开更多
In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling met...In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.展开更多
In this paper two kernel density estimators are introduced and investigated. In order to reduce bias, we intuitively subtract an estimated bias term from ordinary kernel density estimator. The second proposed density ...In this paper two kernel density estimators are introduced and investigated. In order to reduce bias, we intuitively subtract an estimated bias term from ordinary kernel density estimator. The second proposed density estimator is a geometric extrapolation of the first bias reduced estimator. Theoretical properties such as bias, variance and mean squared error are investigated for both estimators. To observe their finite sample performance, a Monte Carlo simulation study based on small to moderately large samples is presented.展开更多
Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in...Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in GIS does not obey the normal distribution but the p-norm distribution with a determinate parameter. Assuming that the error is random and has the same statistical properties, the probability density function of the normal distribution, Laplace distribution and p-norm distribution are derived based on the arithmetic mean axiom, median axiom and p-median axiom, which means that the normal distribution is only one of these distributions but not the least one. Based on this ideal distribution fitness tests such as Skewness and Kurtosis coefficient test, Pearson chi-square chi(2) test and Kolmogorov test for digitized data are conducted. The results show that the error in map digitization obeys the p-norm distribution whose parameter is close to 1.60. A least p-norm estimation and the least square estimation of digitized data are further analyzed, showing that the least p-norm adjustment is better than the least square adjustment for digitized data processing in GIS.展开更多
Previous research has identified specific areas of frequent tropical cyclone activity in the North Atlantic basin. This study examines long-term and decadal spatio-temporal patterns of Atlantic tropical cyclone freque...Previous research has identified specific areas of frequent tropical cyclone activity in the North Atlantic basin. This study examines long-term and decadal spatio-temporal patterns of Atlantic tropical cyclone frequencies from 1944 to 2009, and analyzes categorical and decadal centroid patterns using kernel density estimation (KDE) and centrographic statistics. Results corroborate previous research which has suggested that the Bermuda-Azores anticyclone plays an integral role in the direction of tropical cyclone tracks. Other teleconnections such as the North Atlantic Oscillation (NAO) may also have an impact on tropical cyclone tracks, but at a different temporal resolution. Results expand on existing knowledge of the spatial trends of tropical cyclones based on storm category and time through the use of spatial statistics. Overall, location of peak frequency varies by tropical cyclone category, with stronger storms being more concentrated in narrow regions of the southern Caribbean Sea and Gulf of Mexico, while weaker storms occur in a much larger area that encompasses much of the Caribbean Sea, Gulf of Mexico, and Atlantic Ocean off of the east coast of the United States. Additionally, the decadal centroids of tropical cyclone tracks have oscillated over a large area of the Atlantic Ocean for much of recorded history. Data collected since 1944 can be analyzed confidently to reveal these patterns.展开更多
In this article, we investigate the density of the solution to a class of stochastic functional differential equations by means of Malliavin calculus. Our aim is to provide upper and lower Gaussian estimates for the d...In this article, we investigate the density of the solution to a class of stochastic functional differential equations by means of Malliavin calculus. Our aim is to provide upper and lower Gaussian estimates for the density.展开更多
Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a k...Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.展开更多
Logistic regression is often used to solve linear binary classification problems such as machine vision,speech recognition,and handwriting recognition.However,it usually fails to solve certain nonlinear multi-classifi...Logistic regression is often used to solve linear binary classification problems such as machine vision,speech recognition,and handwriting recognition.However,it usually fails to solve certain nonlinear multi-classification problem,such as problem with non-equilibrium samples.Many scholars have proposed some methods,such as neural network,least square support vector machine,AdaBoost meta-algorithm,etc.These methods essentially belong to machine learning categories.In this work,based on the probability theory and statistical principle,we propose an improved logistic regression algorithm based on kernel density estimation for solving nonlinear multi-classification.We have compared our approach with other methods using non-equilibrium samples,the results show that our approach guarantees sample integrity and achieves superior classification.展开更多
A novel diversity-sampling based nonparametric multi-modal background model is proposed. Using the samples having more popular and various intensity values in the training sequence, a nonparametric model is built for ...A novel diversity-sampling based nonparametric multi-modal background model is proposed. Using the samples having more popular and various intensity values in the training sequence, a nonparametric model is built for background subtraction. According to the related intensifies, different weights are given to the distinct samples in kernel density estimation. This avoids repeated computation using all samples, and makes computation more efficient in the evaluation phase. Experimental results show the validity of the diversity- sampling scheme and robustness of the proposed model in moving objects segmentation. The proposed algorithm can be used in outdoor surveillance systems.展开更多
There have been many papers presenting kernel density estimators for a strictly stationary continuous time process observed over the time interval [0, T ]. However the estimators do not satisfy the property of mean-sq...There have been many papers presenting kernel density estimators for a strictly stationary continuous time process observed over the time interval [0, T ]. However the estimators do not satisfy the property of mean-square continuity if the process is mean-square continuous. In this paper we present a modified kernel estimator and substantiate that the modified estimator satisfies the property of mean-square continuity. In a simulation study the results show the modified estimator is better than the original estimator in some cases.展开更多
In this article, our proposed kernel estimator, named as Gumbel kernel, which broadened the class of non-negative, asymmetric kernel density estimators. Such kernel estimator can be used in nonparametric estimation of...In this article, our proposed kernel estimator, named as Gumbel kernel, which broadened the class of non-negative, asymmetric kernel density estimators. Such kernel estimator can be used in nonparametric estimation of the probability density function (</span><i><span style="font-family:Verdana;">pdf</span></i><span style="font-family:Verdana;">). When the density functions have limited bounded support on [0, ∞) and they are liberated of boundary bias, always non-negative and obtain the optimal rate of convergence for the mean integrated squared error (MISE). The bias, variance and the optimal bandwidth of the proposed estimators are investigated on theoretical grounds as well as on simulation basis. Further, the applicability of the proposed estimator is compared to Weibul</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">l</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> kernel estimator, where performance of newly proposed kernel is outstanding.展开更多
基金Project(61101185) supported by the National Natural Science Foundation of ChinaProject(2011AA1221) supported by the National High Technology Research and Development Program of China
文摘In order to improve the performance of the probability hypothesis density(PHD) algorithm based particle filter(PF) in terms of number estimation and states extraction of multiple targets, a new probability hypothesis density filter algorithm based on marginalized particle and kernel density estimation is proposed, which utilizes the idea of marginalized particle filter to enhance the estimating performance of the PHD. The state variables are decomposed into linear and non-linear parts. The particle filter is adopted to predict and estimate the nonlinear states of multi-target after dimensionality reduction, while the Kalman filter is applied to estimate the linear parts under linear Gaussian condition. Embedding the information of the linear states into the estimated nonlinear states helps to reduce the estimating variance and improve the accuracy of target number estimation. The meanshift kernel density estimation, being of the inherent nature of searching peak value via an adaptive gradient ascent iteration, is introduced to cluster particles and extract target states, which is independent of the target number and can converge to the local peak position of the PHD distribution while avoiding the errors due to the inaccuracy in modeling and parameters estimation. Experiments show that the proposed algorithm can obtain higher tracking accuracy when using fewer sampling particles and is of lower computational complexity compared with the PF-PHD.
文摘A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error of the estimator are studied.
文摘Let (X,Y) be an R^d×R^1 valued random vector (X_1,Y_1),…, (X_n,Y_n) be a random sample drawn from (X,Y), and let E|Y|<∞. The regression function m(x)=E(Y|X=x) for x∈R^d is estimated by where, and h_n is a positive number depending upon n only, nad K is a given nonnegative function on R^d. In the paper, we study the L_p convergence rate of kernel estimate m_n(x) of m(x) in suitable condition, and improve and extend the results of Wei Lansheng.
基金Supported by the Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)Program of Department of Education of Jiangxi Province of China(Grant Nos.GJJ190732,GJJ180737)the Natural Science Foundation Program of Jiangxi Province(Grant No.20202BABL211005).
文摘Assume that f_(n)is the nonparametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere S^(d-1).We established that the large deviation principle for{sup_(x∈S^(d-1))|fn(x)-fn(-x)|,n≥1}holds if the kernel function is a function with bounded variation,and the density function f of the random variables is continuous and symmetric.
基金supported by Natural Science Foun■ion of Henan P■visial Commission of Bdusation
文摘In the paper,we study the strong uniform consistency for the kernal estimates of random window w■th of density function and its derivatives under the condition that the sequence{X_n}of the ■ are the identically Φ-mixing random variabks.
文摘There have been vast amount of studies on background modeling to detect moving objects. Two recent reviews[1,2] showed that kernel density estimation(KDE) method and Gaussian mixture model(GMM) perform about equally best among possible background models. For KDE, the selection of kernel functions and their bandwidths greatly influence the performance. There were few attempts to compare the adequacy of functions for KDE. In this paper, we evaluate the performance of various functions for KDE. Functions tested include almost everyone cited in the literature and a new function, Laplacian of Gaussian(LoG) is also introduced for comparison. All tests were done on real videos with vary-ing background dynamics and results were analyzed both qualitatively and quantitatively. Effect of different bandwidths was also investigated.
基金Research supported by National Natural Science Foundation of China.
文摘Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n).
文摘In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.
基金Supported by the National Science Foundation of China under Grant No.11273013by the Natural Science Foundation of Jilin Province under Grant No.20180101228JC
文摘It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation, which is completely based on data samples, is a long-term issue that has not been well settled so far. There exist analytic formulae of optimal kernel bandwidth, but they cannot be applied directly to data samples,since they depend on the unknown underlying density functions from which the samples are drawn. In this work, we devise an approach to pick out the totally data-based optimal bandwidth. First, we derive correction formulae for the analytic formulae of optimal bandwidth to compute the roughness of the sample's density function. Then substitute the correction formulae into the analytic formulae for optimal bandwidth, and through iteration we obtain the sample's optimal bandwidth. Compared with analytic formulae, our approach gives very good results, with relative differences from the analytic formulae being only 2%～3% for sample size larger than 10~4. This approach can also be generalized easily to cases of variable kernel estimations.
基金Zhou's research was partially supported by the NNSF of China (10471140, 10571169)Wu's research was partially supported by NNSF of China (0571170)
文摘A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.
基金supported by Science and Technology project of the State Grid Corporation of China“Research on Active Development Planning Technology and Comprehensive Benefit Analysis Method for Regional Smart Grid Comprehensive Demonstration Zone”National Natural Science Foundation of China(51607104)
文摘In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.
文摘In this paper two kernel density estimators are introduced and investigated. In order to reduce bias, we intuitively subtract an estimated bias term from ordinary kernel density estimator. The second proposed density estimator is a geometric extrapolation of the first bias reduced estimator. Theoretical properties such as bias, variance and mean squared error are investigated for both estimators. To observe their finite sample performance, a Monte Carlo simulation study based on small to moderately large samples is presented.
文摘Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in GIS does not obey the normal distribution but the p-norm distribution with a determinate parameter. Assuming that the error is random and has the same statistical properties, the probability density function of the normal distribution, Laplace distribution and p-norm distribution are derived based on the arithmetic mean axiom, median axiom and p-median axiom, which means that the normal distribution is only one of these distributions but not the least one. Based on this ideal distribution fitness tests such as Skewness and Kurtosis coefficient test, Pearson chi-square chi(2) test and Kolmogorov test for digitized data are conducted. The results show that the error in map digitization obeys the p-norm distribution whose parameter is close to 1.60. A least p-norm estimation and the least square estimation of digitized data are further analyzed, showing that the least p-norm adjustment is better than the least square adjustment for digitized data processing in GIS.
文摘Previous research has identified specific areas of frequent tropical cyclone activity in the North Atlantic basin. This study examines long-term and decadal spatio-temporal patterns of Atlantic tropical cyclone frequencies from 1944 to 2009, and analyzes categorical and decadal centroid patterns using kernel density estimation (KDE) and centrographic statistics. Results corroborate previous research which has suggested that the Bermuda-Azores anticyclone plays an integral role in the direction of tropical cyclone tracks. Other teleconnections such as the North Atlantic Oscillation (NAO) may also have an impact on tropical cyclone tracks, but at a different temporal resolution. Results expand on existing knowledge of the spatial trends of tropical cyclones based on storm category and time through the use of spatial statistics. Overall, location of peak frequency varies by tropical cyclone category, with stronger storms being more concentrated in narrow regions of the southern Caribbean Sea and Gulf of Mexico, while weaker storms occur in a much larger area that encompasses much of the Caribbean Sea, Gulf of Mexico, and Atlantic Ocean off of the east coast of the United States. Additionally, the decadal centroids of tropical cyclone tracks have oscillated over a large area of the Atlantic Ocean for much of recorded history. Data collected since 1944 can be analyzed confidently to reveal these patterns.
基金supported by Viet Nam National Foundation for Science and Technology Development(NAFOSTED) under grant number 101.03-2015.15supported by the Vietnam National University,Hanoi(QG.16.09)
文摘In this article, we investigate the density of the solution to a class of stochastic functional differential equations by means of Malliavin calculus. Our aim is to provide upper and lower Gaussian estimates for the density.
文摘Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.
基金The authors would like to thank all anonymous reviewers for their suggestions and feedback.This work was supported by National Natural Science Foundation of China(Grant No.61379103).
文摘Logistic regression is often used to solve linear binary classification problems such as machine vision,speech recognition,and handwriting recognition.However,it usually fails to solve certain nonlinear multi-classification problem,such as problem with non-equilibrium samples.Many scholars have proposed some methods,such as neural network,least square support vector machine,AdaBoost meta-algorithm,etc.These methods essentially belong to machine learning categories.In this work,based on the probability theory and statistical principle,we propose an improved logistic regression algorithm based on kernel density estimation for solving nonlinear multi-classification.We have compared our approach with other methods using non-equilibrium samples,the results show that our approach guarantees sample integrity and achieves superior classification.
基金Project supported by National Basic Research Program of Chinaon Urban Traffic Monitoring and Management System(Grant No .TG1998030408)
文摘A novel diversity-sampling based nonparametric multi-modal background model is proposed. Using the samples having more popular and various intensity values in the training sequence, a nonparametric model is built for background subtraction. According to the related intensifies, different weights are given to the distinct samples in kernel density estimation. This avoids repeated computation using all samples, and makes computation more efficient in the evaluation phase. Experimental results show the validity of the diversity- sampling scheme and robustness of the proposed model in moving objects segmentation. The proposed algorithm can be used in outdoor surveillance systems.
基金Project supported by the National Natural Science Foundation of China (Grant No.60773081)the Shanghai Leading Academic Discipline Project (Grant No.S30104)
文摘There have been many papers presenting kernel density estimators for a strictly stationary continuous time process observed over the time interval [0, T ]. However the estimators do not satisfy the property of mean-square continuity if the process is mean-square continuous. In this paper we present a modified kernel estimator and substantiate that the modified estimator satisfies the property of mean-square continuity. In a simulation study the results show the modified estimator is better than the original estimator in some cases.
文摘In this article, our proposed kernel estimator, named as Gumbel kernel, which broadened the class of non-negative, asymmetric kernel density estimators. Such kernel estimator can be used in nonparametric estimation of the probability density function (</span><i><span style="font-family:Verdana;">pdf</span></i><span style="font-family:Verdana;">). When the density functions have limited bounded support on [0, ∞) and they are liberated of boundary bias, always non-negative and obtain the optimal rate of convergence for the mean integrated squared error (MISE). The bias, variance and the optimal bandwidth of the proposed estimators are investigated on theoretical grounds as well as on simulation basis. Further, the applicability of the proposed estimator is compared to Weibul</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">l</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> kernel estimator, where performance of newly proposed kernel is outstanding.
