Density testing in a contaminated sample
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 98 (2007)
Issue (Month): 1 (January)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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- Bissantz, N & Claeskens, Gerda & Holzmann, H & Munk, A, 2007. "Testing for lack of fit in inverse regression - with applications to photonic imaging," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/120463, Katholieke Universiteit Leuven.
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