355 articles – 411 references  [version française]
 HAL: hal-00705796, version 1
 Journal of machine Learning Research W&CP 22 (2012) 264-272
 Wilks' phenomenon and penalized likelihood-ratio test for nonparametric curve registration
 Olivier Collier 1, 2, 3, Arnak Dalalyan 1, 2
 (2012-04-20)
 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.
 1: IMAGINE CSTB – Ecole des Ponts ParisTech – Université Paris-Est Créteil Val-de-Marne (UPEC) 2: Laboratoire d'Informatique Gaspard-Monge (LIGM) Université Paris-Est Marne-la-Vallée (UPEMLV) – ESIEE – Ecole des Ponts ParisTech – Fédération de Recherche Bézout – CNRS : UMR8049 3: Centre de Recherche en Économie et Statistique (CREST) INSEE – École Nationale de la Statistique et de l'Administration Économique
 Subject : Statistics/Machine Learning
 hal-00705796, version 1 http://hal-enpc.archives-ouvertes.fr/hal-00705796 oai:hal-enpc.archives-ouvertes.fr:hal-00705796 From: Arnak Dalalyan <> Submitted on: Friday, 8 June 2012 11:55:44 Updated on: Friday, 8 June 2012 11:55:44