Wilks' phenomenon and penalized likelihood-ratio test for nonparametric curve registration

Olivier Collier 1, 2, 3 Arnak S. Dalalyan 1, 2
1 IMAGINE [Marne-la-Vallée]
LIGM - Laboratoire d'Informatique Gaspard-Monge, CSTB - Centre Scientifique et Technique du Bâtiment, ENPC - École des Ponts ParisTech
Abstract : The problem of curve registration appears in many different areas of applications ranging from neuroscience to road traffic modeling. In the present work, we propose a nonparametric testing framework in which we develop a generalized likelihood ratio test to perform curve registration. We first prove that, under the null hypothesis, the resulting test statistic is asymptotically distributed as a chi-squared random variable. This result, often referred to as Wilks' phenomenon, provides a natural threshold for the test of a prescribed asymptotic significance level and a natural measure of lack-of-fit in terms of the p-value of the $\chi^2$-test. We also prove that the proposed test is consistent, i.e., its power is asymptotically equal to 1. Finite sample properties of the proposed methodology are demonstrated by numerical simulations.
Type de document :
Article dans une revue
Journal of machine Learning Research W&CP, 2012, 22, pp.264-272
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https://hal-enpc.archives-ouvertes.fr/hal-00705796
Contributeur : Arnak Dalalyan <>
Soumis le : vendredi 8 juin 2012 - 11:55:44
Dernière modification le : mercredi 12 septembre 2018 - 01:28:23

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  • HAL Id : hal-00705796, version 1

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Olivier Collier, Arnak S. Dalalyan. Wilks' phenomenon and penalized likelihood-ratio test for nonparametric curve registration. Journal of machine Learning Research W&CP, 2012, 22, pp.264-272. 〈hal-00705796〉

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