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UID:6546@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210208T140000
DTEND;TZID=Europe/Paris:20210208T160000
DTSTAMP:20241120T201736Z
URL:https://www.i2m.univ-amu.fr/evenements/anouar-meynaoui/
SUMMARY: (...): Anouar Meynaoui  (université de Rouen) : Adaptive test of 
 independence based on HSIC measures
DESCRIPTION:: Abstract : \n\nDependence measures based on reproducing kerne
 l Hilbert spaces\, also known as Hilbert-Schmidt Independence Criterion an
 d denoted HSIC\, are widely used to statistically decide whether or not tw
 o random vectors are dependent. Recently\, non-parametric HSIC-based stati
 stical tests of independence have been performed. However\, these tests le
 ad to the question of the choice of the kernels associated to the HSIC. In
  particular\, there is as yet no method to objectively select specific ker
 nels with theoretical guarantees in terms of first and second kind errors.
  One of the main contributions of this work is to develop a new HSIC-based
  aggregated procedure which avoids such a kernel choice\, and to provide t
 heoretical guarantees for this procedure. To achieve this\, we first intro
 duce non-asymptotic single tests based on Gaussian kernels with a given ba
 ndwidth\, which are of prescribed level $\\alpha \\in (0\,1)$. From a theo
 retical point of view\, we upper-bound their uniform separation rate of te
 sting over Sobolev and Nikol'skii balls. Then\, we aggregate several singl
 e tests\, and obtain similar upper-bounds for the uniform separation rate 
 of the aggregated procedure over the same regularity spaces. Another main 
 contribution is that we provide a lower-bound for the non-asymptotic minim
 ax separation rate of testing over Sobolev balls\, and deduce that the agg
 regated procedure is adaptive in the minimax sense over such regularity sp
 aces. Finally\, from a practical point of view\, we perform numerical stud
 ies in order to assess the efficiency of our aggregated procedure and comp
 are it to existing independence tests in the literature. 
CATEGORIES:Séminaire,Statistique
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