Density testing in a contaminated sample

H Holzmann, N Bissantz, A Munk - Journal of multivariate analysis, 2007 - Elsevier
H Holzmann, N Bissantz, A Munk
Journal of multivariate analysis, 2007Elsevier
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 …
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.
Elsevier
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