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Centre de Recherche en Économie et Statistique |  |
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Centre de Recherche en Économie et Statistique | |
| HAL: hal-00705796, version 1 |
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| Journal of machine Learning Research W&CP 22 (2012) 264-272 |
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| Wilks' phenomenon and penalized likelihood-ratio test for nonparametric curve registration |
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| Olivier Collier 1, 2, 3Arnak Dalalyan 1, 2 |
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| (2012-04-20) |
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| 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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| 1: | IMAGINE |
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CSTB – Ecole des Ponts ParisTech – Université Paris-Est Créteil Val-de-Marne (UPEC) |
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| 2: | Laboratoire d'Informatique Gaspard-Monge (LIGM) |
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Université Paris-Est Marne-la-Vallée (UPEMLV) – ESIEE – Ecole des Ponts ParisTech – Fédération de Recherche Bézout – CNRS : UMR8049 |
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| 3: | Centre de Recherche en Économie et Statistique (CREST) |
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INSEE – École Nationale de la Statistique et de l'Administration Économique |
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| 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 | |
