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April 2013 Minimax adaptive tests for the functional linear model
Nadine Hilgert, André Mas, Nicolas Verzelen
Ann. Statist. 41(2): 838-869 (April 2013). DOI: 10.1214/13-AOS1093

Abstract

We introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output. The test statistics combine multiple testing ideas and random projections of the input data through functional principal component analysis. Interestingly, the procedures are completely data-driven and do not require any prior knowledge on the smoothness of the slope nor on the smoothness of the covariate functions. The levels and powers against local alternatives are assessed in a nonasymptotic setting. This allows us to prove that these procedures are minimax adaptive (up to an unavoidable $\log\log n$ multiplicative term) to the unknown regularity of the slope. As a side result, the minimax separation distances of the slope are derived for a large range of regularity classes. A numerical study illustrates these theoretical results.

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Nadine Hilgert. André Mas. Nicolas Verzelen. "Minimax adaptive tests for the functional linear model." Ann. Statist. 41 (2) 838 - 869, April 2013. https://doi.org/10.1214/13-AOS1093

Information

Published: April 2013
First available in Project Euclid: 29 May 2013

zbMATH: 1267.62059
MathSciNet: MR3099123
Digital Object Identifier: 10.1214/13-AOS1093

Subjects:
Primary: 62J05
Secondary: 62G10

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 2 • April 2013
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