Minimax hypothesis testing for curve registration

Olivier Collier
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:236-245, 2012.

Abstract

This paper is concerned with the problem of goodness-of-fit for curve registration, and more precisely for the shifted curve model, whose application field reaches from computer vision and road trafic prediction to medicine. We give bounds for the asymptotic minimax separation rate, when the functions in the alternative lie in Sobolev balls and the separation from the null hypothesis is measured by the l2-norm. We use the generalized likelihood ratio to build a nonadaptive procedure depending on a tuning parameter, which we choose in an optimal way according to the smoothness of the ambient space. Then, a Bonferroni procedure is applied to give an adaptive test over a range of Sobolev balls. Both achieve the asymptotic minimax separation rates, up to possible logarithmic factors.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-collier12, title = {Minimax hypothesis testing for curve registration}, author = {Collier, Olivier}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {236--245}, 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/collier12/collier12.pdf}, url = {https://proceedings.mlr.press/v22/collier12.html}, abstract = {This paper is concerned with the problem of goodness-of-fit for curve registration, and more precisely for the shifted curve model, whose application field reaches from computer vision and road trafic prediction to medicine. We give bounds for the asymptotic minimax separation rate, when the functions in the alternative lie in Sobolev balls and the separation from the null hypothesis is measured by the l2-norm. We use the generalized likelihood ratio to build a nonadaptive procedure depending on a tuning parameter, which we choose in an optimal way according to the smoothness of the ambient space. Then, a Bonferroni procedure is applied to give an adaptive test over a range of Sobolev balls. Both achieve the asymptotic minimax separation rates, up to possible logarithmic factors.} }
Endnote
%0 Conference Paper %T Minimax hypothesis testing for curve registration %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-collier12 %I PMLR %P 236--245 %U https://proceedings.mlr.press/v22/collier12.html %V 22 %X This paper is concerned with the problem of goodness-of-fit for curve registration, and more precisely for the shifted curve model, whose application field reaches from computer vision and road trafic prediction to medicine. We give bounds for the asymptotic minimax separation rate, when the functions in the alternative lie in Sobolev balls and the separation from the null hypothesis is measured by the l2-norm. We use the generalized likelihood ratio to build a nonadaptive procedure depending on a tuning parameter, which we choose in an optimal way according to the smoothness of the ambient space. Then, a Bonferroni procedure is applied to give an adaptive test over a range of Sobolev balls. Both achieve the asymptotic minimax separation rates, up to possible logarithmic factors.
RIS
TY - CPAPER TI - Minimax hypothesis testing for curve registration 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-collier12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 236 EP - 245 L1 - http://proceedings.mlr.press/v22/collier12/collier12.pdf UR - https://proceedings.mlr.press/v22/collier12.html AB - This paper is concerned with the problem of goodness-of-fit for curve registration, and more precisely for the shifted curve model, whose application field reaches from computer vision and road trafic prediction to medicine. We give bounds for the asymptotic minimax separation rate, when the functions in the alternative lie in Sobolev balls and the separation from the null hypothesis is measured by the l2-norm. We use the generalized likelihood ratio to build a nonadaptive procedure depending on a tuning parameter, which we choose in an optimal way according to the smoothness of the ambient space. Then, a Bonferroni procedure is applied to give an adaptive test over a range of Sobolev balls. Both achieve the asymptotic minimax separation rates, up to possible logarithmic factors. ER -
APA
Collier, O.. (2012). Minimax hypothesis testing for curve registration. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:236-245 Available from https://proceedings.mlr.press/v22/collier12.html.

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