A cross-validation bandwidth choice for kernel density estimates with selection biased data

[摘要] This paper studies the risks and bandwidth choices of a kernel estimate of the underlying density when the data are obtained from s independent biased samples. The main results of this paper give the asymptotic representation of the integrated squared errors and the mean integrated squared errors of the estimate and establish a cross-validation criterion for bandwidth selection. This kernel density estimate is shown to be asymptotically superior to many other intuitive kernel density estimates. The data-driven cross-validation bandwidth is shown to be asymptotically optimal in the sense of Stone (1984, Ann. Statist. 12, 1285-1297). The finite sample properties of the cross-validation bandwidth are investigated through a Monte Carlo simulation. (C) 1997 Academic Press.

[发布日期] 1997-04-01

[关键词] kernel density estimate;integrated squared error;bandwidth;nonparametric MLE;weighted distribution;biased sampling model;cross-validation