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Article Dans Une Revue Journal of Machine Learning Research Année : 2012

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

Olivier Collier
• Fonction : Auteur
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Arnak S. Dalalyan

#### Résumé

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.

#### Domaines

Statistiques [stat] Machine Learning [stat.ML]

### Dates et versions

hal-00705796 , version 1 (08-06-2012)

### Identifiants

• HAL Id : hal-00705796 , version 1

### Citer

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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