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

Arnak Dalalyan, Olivier Collier
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 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, extiti.e., its power is asymptotically equal to 1. Finite sample properties of the proposed methodology are demonstrated by numerical simulations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-dalalyan12, title = {Wilks' phenomenon and penalized likelihood-ratio test for nonparametric curve registration}, author = {Dalalyan, Arnak and Collier, Olivier}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {264--272}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/dalalyan12/dalalyan12.pdf}, url = {https://proceedings.mlr.press/v22/dalalyan12.html}, 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, extiti.e., its power is asymptotically equal to 1. Finite sample properties of the proposed methodology are demonstrated by numerical simulations.} }
Endnote
%0 Conference Paper %T Wilks’ phenomenon and penalized likelihood-ratio test for nonparametric curve registration %A Arnak Dalalyan %A Olivier Collier %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-dalalyan12 %I PMLR %P 264--272 %U https://proceedings.mlr.press/v22/dalalyan12.html %V 22 %X 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, extiti.e., its power is asymptotically equal to 1. Finite sample properties of the proposed methodology are demonstrated by numerical simulations.
RIS
TY - CPAPER TI - Wilks’ phenomenon and penalized likelihood-ratio test for nonparametric curve registration AU - Arnak Dalalyan AU - Olivier Collier BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-dalalyan12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 264 EP - 272 L1 - http://proceedings.mlr.press/v22/dalalyan12/dalalyan12.pdf UR - https://proceedings.mlr.press/v22/dalalyan12.html AB - 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, extiti.e., its power is asymptotically equal to 1. Finite sample properties of the proposed methodology are demonstrated by numerical simulations. ER -
APA
Dalalyan, A. & Collier, O.. (2012). Wilks’ phenomenon and penalized likelihood-ratio test for nonparametric curve registration. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:264-272 Available from https://proceedings.mlr.press/v22/dalalyan12.html.

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