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ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE 认领 引用
1
作者 林正炎 《Acta Mathematica Scientia》 SCIE 2003年第3期345-350,共6页
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
关键词 Associated random variables negatively associated random variables kernel estimate of a density function central limit theorem
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APPROXIMATION RATES OF ERROR DISTRIBUTION OF DOUBLE KERNEL ESTIMATES OF CONDITIONAL DENSITY 认领 引用
2
作者 XueLiugen CaiGuoliang 《Applied Mathematics(A Journal of Chinese Universities)》 2000年第4期425-432,共8页
In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to con... In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) . 展开更多
关键词 Conditional density function double kernel estimator random weighting method approximation rate.
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A KERNEL ESTIMATOR OF A DENSITY FUNCTION IN MULTIVARIATE CASE FROM RANDOMLY CENSORED DATA 认领 引用
3
作者 周勇 《Acta Mathematica Scientia》 SCIE 1996年第2期170-180,共11页
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
关键词 Kernel density estimator asymptotic normality product-limit estimator,mean square error and censored data.
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Dynamic parameters prediction of the spatial deployable mechanism:a hybrid approach combining physics-based and data-driven models 认领 引用
4
作者 Yanhe Tao Qintao Guo +4 位作者 Jin Zhou Cheng Yi You Zhang Xiaofei Liu Ruiqi Chen 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第5期535-549,共15页
Accurate prediction of the spatial mechanism's dynamic parameters in microgravity deployment simulations is crucial for identifying potential faults and ensuring precise gravitational compensation.Traditional engi... Accurate prediction of the spatial mechanism's dynamic parameters in microgravity deployment simulations is crucial for identifying potential faults and ensuring precise gravitational compensation.Traditional engineering models are often inaccurate,primarily because of insufficient experimental data and incomplete understanding of physical phenomena,which impedes model bias reduction in information-poor scenarios.We present a novel hybrid approach aimed at improving the predictive accuracy of the dynamic behavior of spatial deployable mechanisms.The graph convolutional network-temporal convolutional network(GCN-TCN)model,a type of deep learning architecture,is utilized for its expertise in forecasting spatio-temporal data through multi-step predictions.Next,the adaptive bandwidth kernel density estimation technique is applied to estimate the probability density function of residuals from the testing set of the GCN-TCN,quantifying predictive uncertainty.The predictive information is further refined using Bayesian inference,integrating a priori knowledge from physics-based models with data from data-driven models to yield robust posterior predictions.The proposed methodology is validated and shown to be robust through rigorous numerical simulations and experimental validation,demonstrating its ability to provide accurate and reliable predictions for the deployment of spatial mechanisms. 展开更多
关键词 Deep learning Kernel density estimation Data fusion Spatial deployable mechanisms Uncertainty quantification Hybrid approach Bayesian
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On the L_p Convergence Rate of Kernel Estimates for the Nonparametric Regression Function 认领 引用
5
作者 薛留根 《Chinese Quarterly Journal of Mathematics》 1992年第1期37-43,共7页
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
关键词 regression function L convergence rate kernel estimate
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DENSITY ESTIMATES FOR SOLUTIONS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS 认领 引用
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作者 Nguyen Tien DUNG Ta Cong SON +2 位作者 Tran Manh CUONG Nguyen Van TAN Trinh Nhu QUYNH 《Acta Mathematica Scientia》 SCIE CSCD 2019年第4期955-970,共16页
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
关键词 Stochastic functional differential equations density estimates Malliavin calculus
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Performance Evaluation of Various Functions for Kernel Density Estimation 认领 引用 被引量：1
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作者 Youngsung Soh Yongsuk Hae +2 位作者 Aamer Mehmood Raja Hadi Ashraf Intaek Kim 《Open Journal of Applied Sciences》 2013年第1期58-64,共7页
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
关键词 Background Model Kernel Density Estimation Kernel Functions
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Spatiotemporal Patterns of Road Network and Road Development Pri-ority in Three Parallel Rivers Region in Yunnan,China:An Evaluation Based on Modified Kernel Distance Estimate 认领 引用 被引量：7
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作者 YING Lingxiao SHEN Zehao +3 位作者 CHEN Jiding FANG Rui CHEN Xueping JIANG Rui 《Chinese Geographical Science》 SCIE CSCD 2014年第1期39-49,共11页
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
关键词 road network kernel density estimate（KDE） road service road development priority（RDP） Three Parallel Rivers Region China
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Probability distribution of wind power volatility based on the moving average method and improved nonparametric kernel density estimation 认领 引用 被引量：5
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作者 Peizhe Xin Ying Liu +2 位作者 Nan Yang Xuankun Song Yu Huang 《Global Energy Interconnection》 EI 2020年第3期247-258,共12页
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
关键词 Moving average method Signal decomposition Wind power fluctuation characteristics Kernel density estimation Constrained order optimization
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Strong Consistency for the Kernal Estimates of the Random Window Width of the Density Function and its Derivatives Under Φ-Mixing Samples 认领 引用
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作者 樊家琨 《Chinese Quarterly Journal of Mathematics》 1993年第3期52-56,共5页
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
关键词 Φ-mixing sample probability density function random window width kemal estimate strng uniform consistency
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Data-Based Optimal Bandwidth for Kernel Density Estimation of Statistical Samples 认领 引用 被引量：4
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作者 Zhen-Wei Li Ping He 《Communications in Theoretical Physics》 SCIE CAS CSCD 2018年第12期728-734,共7页
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
关键词 numerical methods kernel density estimation optimal bandwidth large-scale structure of Universe
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A KERNEL-TYPE ESTIMATOR OF A QUANTILE FUNCTION UNDER RANDOMLY TRUNCATED DATA 认领 引用 被引量：2
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作者 周勇 吴国富 李道纪 《Acta Mathematica Scientia》 SCIE 2006年第4期585-594,共10页
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
关键词 Truncated data Product-limits quantile function kernel estimator Bahadur representation
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Probability density function and estimation for error of digitized map coordinates in GIS 认领 引用 被引量：1
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作者 童小华 刘大杰 《Journal of Central South University of Technology》 2004年第1期69-74,共6页
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
关键词 probability density function distribution fitness test least p-norm estimation
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AN EFFECTIVE IMAGE RETRIEVAL METHOD BASED ON KERNEL DENSITY ESTIMATION OF COLLAGE ERROR AND MOMENT INVARIANTS 认领 引用 被引量：1
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作者 Zhang Qin Huang Xiaoqing +2 位作者 Liu Wenbo Zhu Yongjun Le Jun 《Journal of Electronics(China)》 2013年第4期391-400,共10页
In this paper, we propose a new method that combines collage error in fractal domain and Hu moment invariants for image retrieval with a statistical method - variable bandwidth Kernel Density Estimation (KDE). The pro... In this paper, we propose a new method that combines collage error in fractal domain and Hu moment invariants for image retrieval with a statistical method - variable bandwidth Kernel Density Estimation (KDE). The proposed method is called CHK (KDE of Collage error and Hu moment) and it is tested on the Vistex texture database with 640 natural images. Experimental results show that the Average Retrieval Rate (ARR) can reach into 78.18%, which demonstrates that the proposed method performs better than the one with parameters respectively as well as the commonly used histogram method both on retrieval rate and retrieval time. 展开更多
关键词 Fractal Coding （FC） Hu moment invariant Kernel Density Estimation （KDE） Variableoptimized bandwidth Image retrieval
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Large Deviations for a Test of Symmetry Based on Kernel Density Estimator of Directional Data 认领 引用
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作者 Mingzhou XU Kun CHENG 《Journal of Mathematical Research with Applications》 CSCD 2021年第6期639-647,共9页
Assume that fnis 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 fnis 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 Sd-1.We established that the large deviation principle for{supx∈Sd-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
关键词 symmetry test kernel density estimator directional data large deviations
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Functional Kernel Estimation of the Conditional Extreme Quantile under Random Right Censoring 认领 引用 被引量：1
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作者 Justin Ushize Rutikanga Aliou Diop 《Open Journal of Statistics》 2021年第1期162-177,共16页
The study of estimation of conditional extreme quantile in incomplete data frameworks is of growing interest. Specially, the estimation of the extreme value index in a censorship framework has been the purpose of many... The study of estimation of conditional extreme quantile in incomplete data frameworks is of growing interest. Specially, the estimation of the extreme value index in a censorship framework has been the purpose of many investigations when finite dimension covariate information has been considered. In this paper, the estimation of the conditional extreme quantile of a heavy-tailed distribution is discussed when some functional random covariate (i.e. valued in some infinite-dimensional space) information is available and the scalar response variable is right-censored. A Weissman-type estimator of conditional extreme quantiles is proposed and its asymptotic normality is established under mild assumptions. A simulation study is conducted to assess the finite-sample behavior of the proposed estimator and a comparison with two simple estimations strategies is provided. 展开更多
关键词 Kernel Estimator Functional Data Censored Data Conditional Extreme Quantile Heavy-Tailed Distributions
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Kernel Density Estimation of Tropical Cyclone Frequencies in the North Atlantic Basin 认领 引用 被引量：1
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作者 Timothy A. Joyner Robert V. Rohli 《International Journal of Geosciences》 CAS 2010年第3期121-129,共9页
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
关键词 Atlantic Tropical Cyclone Frequencies Decadal Centroid Patterns Kernel Density Estimation (KDE) Centrographic Statistics Bermuda-Azores Anticyclone Teleconnections
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Some Improvement on Convergence Rates of Kernel Density Estimator 认领 引用 被引量：1
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作者 Xiaoran Xie Jingjing Wu 《Applied Mathematics》 2014年第11期1684-1696,共13页
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
关键词 Kernel Density Estimation Geometric Extrapolation Bias Reduction Mean Squared Error Convergence Rate
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Optimization Strategy of Commercial Space in Xianyukou Hutong Based on Kernel Density and Space Syntax 认领 引用
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作者 Qiqi Xiong Yi Zheng Bo Zhang 《Journal of World Architecture》 2022年第6期40-48,共9页
Beijing Xianyukou Hutong(hutong refers to historical and cultural block in Chinese)occupies an important geographical location with unique urban fabric,and after years of renewal and protection,the commercial space of... Beijing Xianyukou Hutong(hutong refers to historical and cultural block in Chinese)occupies an important geographical location with unique urban fabric,and after years of renewal and protection,the commercial space of Xianyukou Street and has gained some recognition.This article Xianyukou takes commercial hutong in Beijing as an example,spatial analysis was carried out using methods like GIS kernel density method,space syntax after site investigation and research.Based on the street space problems found,this paper then puts forward strategies to improve and upgrade Xianyukou Street’s commercial space and improve businesses in Xianyukou Street and other similar hutong. 展开更多
关键词 Hutong Xianyukou Street Commercial space Space syntax Kernel density estimation
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Strong Convergence Rates of Double Kernel Estimates of Conditional Desity Under Stationary Sequences 认领 引用 被引量：1
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作者 薛留根 李雪臣 马全甫 《Chinese Quarterly Journal of Mathematics》 1999年第2期1-10,共10页
In the paper,we study the strong convergence rates of double kernel estimates of conditional density under stationary sequences.
关键词 conditional density double kernel estimates strong convergence rates stationary sequences
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