Density testing in a contaminated sample

Hajo Holzmann, Nicolai Bissantz and Axel Munk

Journal of Multivariate Analysis, 2007, vol. 98, issue 1, 57-75

Abstract: We study non-parametric tests for checking parametric hypotheses about a multivariate density f of independent identically distributed random vectors Z1,Z2,... which are observed under additional noise with density [psi]. 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 Zi. 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.

Keywords: Asymptotic; normality; Deconvolution; Goodness; of; fit; Integrated; square; error; Multivariate; nonparametric; density; estimation (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (6)

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