Density testing in a contaminated sample

JOURNAL OF MULTIVARIATE ANALYSIS

卷:98

Article

Holzmann, Hajo ; Bissantz, Nicolai ; Munk, Axel

关键词: asymptotic normality;    deconvolution;    goodness of fit;    integrated square error;    multivariate nonparametric density estimation;   

DOI  :  10.1016/j.jmva.2005.09.010

来源: Elsevier

【 摘 要 】

We study non-parametric tests for checking parametric hypotheses about a multivariate density f of independent identically distributed random vectors Z(1), Z(2),... which are observed under additional noise with density. The tests we propose are an extension of the test due to Bickel and Rosenblatt [On some global measures of the deviations of density function estimates, Ann. Statist. 1 (1973) 1071-1095] and are based on a comparison of a nonparametric deconvolution estimator and the smoothed version of a parametric fit of the density f of the variables of interest Z(i). In an example the loss of efficiency is highlighted when the test is based on the convolved (but observable) density g = f * psi instead on the initial density of interest f. (C) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free