Central limit theorem for the variable bandwidth kernel density estimators

被引：0
作者：
Janet Nakarmi
Hailin Sang
机构：
[1] University of Central Arkansas,Department of Mathematics
[2] The University of Mississippi,Department of Mathematics
来源：
Journal of the Korean Statistical Society | 2018年 / 47卷
关键词：
primary 62G07; secondary 62E20; Central limit theorem; Variable bandwidth kernel density estimation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we study the ideal variable bandwidth kernel density estimator introduced by McKay (1993a, b) and Jones et al. (1994) and the plug-in practical version of the variable bandwidth kernel estimator with two sequences of bandwidths as in Giné and Sang (2013). Based on the bias and variance analysis of the ideal and plug-in variable bandwidth kernel density estimators, we study the central limit theorems for each of them. The simulation study confirms the central limit theorem and demonstrates the advantage of the plug-in variable bandwidth kernel method over the classical kernel method.
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页码：201 / 215
页数：14
相关论文
共 18 条
[1]  
Abramson I(1982)On bandwidth variation in kernel estimates - a square-root law Ann. Statist. 10 1217-1223
[2]  
Giné E(2002)Rates of strong uniform consistency for multivariate kernel density estimators Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 38 907-921
[3]  
Guillou A(2010)Uniform asymptotics for kernel density estimators with variable bandwidths J. Nonparametr. Stat. 22 773-795
[4]  
Giné E(1995)Improved variable window kernel estimates of probability densities Ann. Statist. 23 1-10
[5]  
Sang H(1988)Variable window width kernel estimates of probability densities Probab. Theory Related Fields 80 37-49
[6]  
Hall P(1994)Variable location and scale kernel density estimation Ann. Inst. Statist. Math. 46 521-535
[7]  
Hu T(1994)Visual understanding of higher order kernels Journal of Computational and Graphical Statistics 3 447-458
[8]  
Marron J S(1993)A note on bias reduction in variable kernel density estimates The Canadian Journal of Statistics 21 367-375
[9]  
Hall P(1999)A generalized kernel density estimator Teoriya Veroyatnosteĭ ee Primeneniya 44 634-645
[10]  
Marron J S(1992)Variable kernel density estimation Ann. Statist. 20 1236-1265
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