Electronic Journal of Statistics

Minimax hypothesis testing for curve registration

Olivier Collier

Full-text: Open access

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 traffic 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 $l_{2}$-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.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 1129-1154.

Dates
First available in Project Euclid: 29 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1340974138

Digital Object Identifier
doi:10.1214/12-EJS706

Mathematical Reviews number (MathSciNet)
MR2988441

Zentralblatt MATH identifier
1334.62077

Keywords
Adaptive testing composite null hypothesis generalized maximum likelihood minimax hypothesis testing

Citation

Collier, Olivier. Minimax hypothesis testing for curve registration. Electron. J. Statist. 6 (2012), 1129--1154. doi:10.1214/12-EJS706. https://projecteuclid.org/euclid.ejs/1340974138


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