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 χ 2 -test. We also prove that the proposed test is consistent, i.e. ,i ts power is asymptotically equal to 1. Finite sample properties of the proposed methodology are demonstrated by numerical simulations.
['Arnak S. Dalalyan', 'Olivier Collier']
Wilks' phenomenon and penalized likelihood-ratio test for nonparametric curve registration