Optimal bandwidth selection for multivariate kernel deconvolution density estimation

被引：0
作者：
Élie Youndjé
Martin T. Wells
机构：
[1] Université de Rouen,Laboratoire de Mathématiques Raphaël Salem
[2] Cornell University,Department of Social Statistics
来源：
TEST | 2008年 / 17卷
关键词：
Density estimation; Deconvolution; Cross-validation; Asymptotic optimality; 62F03; 62E17; 62P25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Assume we have i.i.d. replications from the mismeasured random vector Y=X+ε, where X and ε are mutually independent. We consider a data-driven bandwidth, based on a cross-validation ideas, for multivariate kernel deconvolution estimator of the density of X. The proposed data-driven bandwidth selection method is shown to be asymptotically optimal. As a by-product of the proof of this result, we show that the average squared error, the integrated squared error, and the mean integrated squared error are asymptotically equivalent error measures.
引用
收藏
页码：138 / 162
页数：24
相关论文
共 31 条
[1]  
Barry J(1995)Choosing the smoothing parameter in a Fourier approach to nonparametric deconvolution of a density estimate J Nonparametric Stat 4 223-232
[2]  
Diggle P(1984)An alternative method of cross-validation for the smoothing of density estimates Biometrika 71 353-360
[3]  
Bowman AW(1988)Optimal rates of convergence for deconvolving a density J Am Stat Assoc 83 1184-1186
[4]  
Carroll RJ(2004)Bootstrap bandwidth selection in kernel density estimation from a contaminated sample Ann Inst Stat Math 56 19-47
[5]  
Hall P(2004)Practical bandwidth selection in deconvolution kernel density estimation Comput Stat Data Anal 45 249-267
[6]  
Delaigle A(1993)A Fourier approach to nonparametric deconvolution of a density estimate J Roy Stat Soc Ser B 55 523-531
[7]  
Gijbels I(1991)Asymptotic normality for deconvolution kernel density estimators Sankhyā Ser A 53 97-110
[8]  
Delaigle A(1991)On the optimal rates of convergence for nonparametric deconvolution problems Ann Stat 19 1257-1272
[9]  
Gijbels I(1982)Limit theorems for stochastic measures of the accuracy of density estimators Stoch Process Appl 13 11-25
[10]  
Diggle PJ(1983)Large sample optimality of least squares cross-validation in density estimation Ann Stat 11 1156-1174
1234