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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.
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Soumis le : vendredi 8 juin 2012 - 11:55:44
Dernière modification le : vendredi 5 août 2022 - 14:49:41


  • HAL Id : hal-00705796, version 1


Olivier Collier, Arnak S. Dalalyan. Wilks' phenomenon and penalized likelihood-ratio test for nonparametric curve registration. Journal of Machine Learning Research, 2012, 22, pp.264-272. ⟨hal-00705796⟩



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