Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove mod...Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.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 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
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
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
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 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
The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data.Two c...The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data.Two commonly used tools are the kernel density estimation and reduced chi-squared statistic used in combination with a weighted mean.Due to the wide applicability of these tools,we present a Java-based computer application called KDX to facilitate the visualization of data and the utilization of these numerical tools.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
This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author als...This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author also found that the estimators show remarkable in the small sample case yet.展开更多
Road network is a critical component of public infrastructure,and the supporting system of social and economic development.Based on a modified kernel density estimate(KDE)algorithm,this study evaluated the road servic...Road network is a critical component of public infrastructure,and the supporting system of social and economic development.Based on a modified kernel density estimate(KDE)algorithm,this study evaluated the road service capacity provided by a road network composed of multi-level roads(i.e.national,provincial,county and rural roads),by taking account of the differences of effect extent and intensity for roads of different levels.Summarized at town scale,the population burden and the annual rural economic income of unit road service capacity were used as the surrogates of social and economic demands for road service.This method was applied to the road network of the Three Parallel River Region,the northwestern Yunnan Province,China to evaluate the development of road network in this region.In results,the total road length of this region in 2005 was 3.70×104km,and the length ratio between national,provincial,county and rural roads was 1∶2∶8∶47.From 1989 to 2005,the regional road service capacity increased by 13.1%,of which the contributions from the national,provincial,county and rural roads were 11.1%,19.4%,22.6%,and 67.8%,respectively,revealing the effect of′All Village Accessible′policy of road development in the mountainous regions in the last decade.The spatial patterns of population burden and economic requirement of unit road service suggested that the areas farther away from the national and provincial roads have higher road development priority(RDP).Based on the modified KDE model and the framework of RDP evaluation,this study provided a useful approach for developing an optimal plan of road development at regional scale.展开更多
An improved method using kernel density estimation （KDE） and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only smal...An improved method using kernel density estimation （KDE） and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only small samples can be used due to the high costs of experimental measurements. However, model validation provides more confidence for decision makers when improving prediction accuracy at the same time. The confidence level method is introduced and the optimum sample variance is determined using a new method in kernel density estimation to increase the credibility of model validation. As a numerical example, the static frame model validation challenge problem presented by Sandia National Laboratories has been chosen. The optimum bandwidth is selected in kernel density estimation in order to build the probability model based on the calibration data. The model assessment is achieved using validation and accreditation experimental data respectively based on the probability model. Finally, the target structure prediction is performed using validated model, which are consistent with the results obtained by other researchers. The results demonstrate that the method using the improved confidence level and kernel density estimation is an effective approach to solve the model validation problem with small samples.展开更多
The accurate estimation of road traffic states can provide decision making for travelers and traffic managers. In this work,an algorithm based on kernel-k nearest neighbor(KNN) matching of road traffic spatial charact...The accurate estimation of road traffic states can provide decision making for travelers and traffic managers. In this work,an algorithm based on kernel-k nearest neighbor(KNN) matching of road traffic spatial characteristics is presented to estimate road traffic states. Firstly, the representative road traffic state data were extracted to establish the reference sequences of road traffic running characteristics(RSRTRC). Secondly, the spatial road traffic state data sequence was selected and the kernel function was constructed, with which the spatial road traffic data sequence could be mapped into a high dimensional feature space. Thirdly, the referenced and current spatial road traffic data sequences were extracted and the Euclidean distances in the feature space between them were obtained. Finally, the road traffic states were estimated from weighted averages of the selected k road traffic states, which corresponded to the nearest Euclidean distances. Several typical links in Beijing were adopted for case studies. The final results of the experiments show that the accuracy of this algorithm for estimating speed and volume is 95.27% and 91.32% respectively, which prove that this road traffic states estimation approach based on kernel-KNN matching of road traffic spatial characteristics is feasible and can achieve a high accuracy.展开更多
The application of high-performance imaging sensors in space-based space surveillance systems makes it possible to recognize space objects and estimate their poses using vision-based methods. In this paper, we propose...The application of high-performance imaging sensors in space-based space surveillance systems makes it possible to recognize space objects and estimate their poses using vision-based methods. In this paper, we proposed a kernel regression-based method for joint multi-view space object recognition and pose estimation. We built a new simulated satellite image dataset named BUAA-SID 1.5 to test our method using different image representations. We evaluated our method for recognition-only tasks, pose estimation-only tasks, and joint recognition and pose estimation tasks. Experimental results show that our method outperforms the state-of-the-arts in space object recognition, and can recognize space objects and estimate their poses effectively and robustly against noise and lighting conditions.展开更多
A new algorithm for linear instantaneous independent component analysis is proposed based on maximizing the log-likelihood contrast function which can be changed into a gradient equation.An iterative method is introdu...A new algorithm for linear instantaneous independent component analysis is proposed based on maximizing the log-likelihood contrast function which can be changed into a gradient equation.An iterative method is introduced to solve this equation efficiently.The unknown probability density functions as well as their first and second derivatives in the gradient equation are estimated by kernel density method.Computer simulations on artificially generated signals and gray scale natural scene images confirm the efficiency and accuracy of the proposed algorithm.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, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bia...In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.展开更多
Single image motion deblurring has been a very challenging problem in the field of image processing. Although there are many researches had been proposed to solve this problem, it still has problems on kernel accuracy...Single image motion deblurring has been a very challenging problem in the field of image processing. Although there are many researches had been proposed to solve this problem, it still has problems on kernel accuracy. In order to improve the kernel accuracy, an effective structure selection method was used to select the salient structure of the blur image. Then a novel kernel estimation method based on L0-2 norm was proposed. To guarantee the sparse kernel and eliminate the negative influence of details L0-norm was used. And L2-norm was used to ensure the continuity of kernel. Many experiments were done to compare proposed method and state-of-the-art methods. The results show that our method can estimate a better kernel and use less time than previous work, especially when the size of blur kernel is large.展开更多
In this paper, regression function estimation from independent and identically distributed data is considered. We establish strong pointwise consistency of the famous Nadaraya-Watson estimator under weaker conditions ...In this paper, regression function estimation from independent and identically distributed data is considered. We establish strong pointwise consistency of the famous Nadaraya-Watson estimator under weaker conditions which permit to apply kernels with unbounded support and even not integrable ones and provide a general approach for constructing strongly consistent kernel estimates of regression functions.展开更多
基金Research supported by the National Natural Science Foundation of China (10271091)
文摘Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.
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.
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.
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.
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.
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.
文摘The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data.Two commonly used tools are the kernel density estimation and reduced chi-squared statistic used in combination with a weighted mean.Due to the wide applicability of these tools,we present a Java-based computer application called KDX to facilitate the visualization of data and the utilization of these numerical tools.
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.
文摘This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author also found that the estimators show remarkable in the small sample case yet.
基金Under the auspices of National Natural Science Foundation of China(No.41371190,31021001)Scientific and Tech-nical Projects of Western China Transportation Construction,Ministry of Transport of China(No.2008-318-799-17)
文摘Road network is a critical component of public infrastructure,and the supporting system of social and economic development.Based on a modified kernel density estimate(KDE)algorithm,this study evaluated the road service capacity provided by a road network composed of multi-level roads(i.e.national,provincial,county and rural roads),by taking account of the differences of effect extent and intensity for roads of different levels.Summarized at town scale,the population burden and the annual rural economic income of unit road service capacity were used as the surrogates of social and economic demands for road service.This method was applied to the road network of the Three Parallel River Region,the northwestern Yunnan Province,China to evaluate the development of road network in this region.In results,the total road length of this region in 2005 was 3.70×104km,and the length ratio between national,provincial,county and rural roads was 1∶2∶8∶47.From 1989 to 2005,the regional road service capacity increased by 13.1%,of which the contributions from the national,provincial,county and rural roads were 11.1%,19.4%,22.6%,and 67.8%,respectively,revealing the effect of′All Village Accessible′policy of road development in the mountainous regions in the last decade.The spatial patterns of population burden and economic requirement of unit road service suggested that the areas farther away from the national and provincial roads have higher road development priority(RDP).Based on the modified KDE model and the framework of RDP evaluation,this study provided a useful approach for developing an optimal plan of road development at regional scale.
基金Funding of Jiangsu Innovation Program for Graduate Education (CXZZ11_0193)NUAA Research Funding (NJ2010009)
文摘An improved method using kernel density estimation （KDE） and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only small samples can be used due to the high costs of experimental measurements. However, model validation provides more confidence for decision makers when improving prediction accuracy at the same time. The confidence level method is introduced and the optimum sample variance is determined using a new method in kernel density estimation to increase the credibility of model validation. As a numerical example, the static frame model validation challenge problem presented by Sandia National Laboratories has been chosen. The optimum bandwidth is selected in kernel density estimation in order to build the probability model based on the calibration data. The model assessment is achieved using validation and accreditation experimental data respectively based on the probability model. Finally, the target structure prediction is performed using validated model, which are consistent with the results obtained by other researchers. The results demonstrate that the method using the improved confidence level and kernel density estimation is an effective approach to solve the model validation problem with small samples.
基金Projects(LQ16E080012,LY14F030012)supported by the Zhejiang Provincial Natural Science Foundation,ChinaProject(61573317)supported by the National Natural Science Foundation of ChinaProject(2015001)supported by the Open Fund for a Key-Key Discipline of Zhejiang University of Technology,China
文摘The accurate estimation of road traffic states can provide decision making for travelers and traffic managers. In this work,an algorithm based on kernel-k nearest neighbor(KNN) matching of road traffic spatial characteristics is presented to estimate road traffic states. Firstly, the representative road traffic state data were extracted to establish the reference sequences of road traffic running characteristics(RSRTRC). Secondly, the spatial road traffic state data sequence was selected and the kernel function was constructed, with which the spatial road traffic data sequence could be mapped into a high dimensional feature space. Thirdly, the referenced and current spatial road traffic data sequences were extracted and the Euclidean distances in the feature space between them were obtained. Finally, the road traffic states were estimated from weighted averages of the selected k road traffic states, which corresponded to the nearest Euclidean distances. Several typical links in Beijing were adopted for case studies. The final results of the experiments show that the accuracy of this algorithm for estimating speed and volume is 95.27% and 91.32% respectively, which prove that this road traffic states estimation approach based on kernel-KNN matching of road traffic spatial characteristics is feasible and can achieve a high accuracy.
基金co-supported by the National Natural Science Foundation of China (Grant Nos. 61371134, 61071137)the National Basic Research Program of China (No. 2010CB327900)
文摘The application of high-performance imaging sensors in space-based space surveillance systems makes it possible to recognize space objects and estimate their poses using vision-based methods. In this paper, we proposed a kernel regression-based method for joint multi-view space object recognition and pose estimation. We built a new simulated satellite image dataset named BUAA-SID 1.5 to test our method using different image representations. We evaluated our method for recognition-only tasks, pose estimation-only tasks, and joint recognition and pose estimation tasks. Experimental results show that our method outperforms the state-of-the-arts in space object recognition, and can recognize space objects and estimate their poses effectively and robustly against noise and lighting conditions.
文摘A new algorithm for linear instantaneous independent component analysis is proposed based on maximizing the log-likelihood contrast function which can be changed into a gradient equation.An iterative method is introduced to solve this equation efficiently.The unknown probability density functions as well as their first and second derivatives in the gradient equation are estimated by kernel density method.Computer simulations on artificially generated signals and gray scale natural scene images confirm the efficiency and accuracy of the proposed algorithm.
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, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.
文摘Single image motion deblurring has been a very challenging problem in the field of image processing. Although there are many researches had been proposed to solve this problem, it still has problems on kernel accuracy. In order to improve the kernel accuracy, an effective structure selection method was used to select the salient structure of the blur image. Then a novel kernel estimation method based on L0-2 norm was proposed. To guarantee the sparse kernel and eliminate the negative influence of details L0-norm was used. And L2-norm was used to ensure the continuity of kernel. Many experiments were done to compare proposed method and state-of-the-art methods. The results show that our method can estimate a better kernel and use less time than previous work, especially when the size of blur kernel is large.
文摘In this paper, regression function estimation from independent and identically distributed data is considered. We establish strong pointwise consistency of the famous Nadaraya-Watson estimator under weaker conditions which permit to apply kernels with unbounded support and even not integrable ones and provide a general approach for constructing strongly consistent kernel estimates of regression functions.
