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Tests non-paramétriques de non-effet et d'adéquation pour des covariables fonctionnelles.

Le : 04/06/2012 11h00
Par : Matthieu Saumard (Rennes 1)
Lieu : I 103
Lien web :
Résumé : We study the problem of nonparametric testing for the effect of a random functional covariate on a response variable. The covariate and the response take values in $L^2[0, 1]$, the Hilbert space of the square-integrable real-valued functions on the unit interval. Our test is based on the remark that checking the no-effect of the functional covariate is equivalent to checking the nullity of the conditional expectation of the response variable given a sufficiently rich set of projections of the covariate. For such finite-dimension search and nonparametric check we use a kernel-based approach. As a result, our test statistic is a quadratic form based on univariate kernel smoothing and the asymptotic critical values are given by the standard normal law. The test is able to detect nonparametric alternatives, including the polynomial ones. The response variable could present heteroscedasticity of unknown form. We do no require the law of the covariate X to be known.