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

Arnak Dalalyan, Olivier Collier ; JMLR W&CP 22: 264-272, 2012.

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 (Wilks' phenomenon). We also prove that the proposed test is consistent, extit{i.e.}, its power is asymptotically equal to $1$. Finite sample properties of the proposed methodology are demonstrated by numerical simulations.