Density testing in a contaminated sample
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 ψ. 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 * ψ instead on the initial density of interest f.
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