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Februrary 2003 Adaptive tests of linear hypotheses by model selection
Y. Baraud, S. Huet, B. Laurent
Ann. Statist. 31(1): 225-251 (Februrary 2003). DOI: 10.1214/aos/1046294463


We propose a new test, based on model selection methods, for testing that the expectation of a Gaussian vector with n independent components belongs to a linear subspace of $\R^{n}$ against a nonparametric alternative. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on the alternative. The properties of the test are nonasymptotic and we prove that the test is rate optimal [up to a possible log(n factor] over various classes of alternatives simultaneously. We also provide a simulation study in order to evaluate the procedure when the purpose is to test goodness-of-fit in a regression model.


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Y. Baraud. S. Huet. B. Laurent. "Adaptive tests of linear hypotheses by model selection." Ann. Statist. 31 (1) 225 - 251, Februrary 2003.


Published: Februrary 2003
First available in Project Euclid: 26 February 2003

zbMATH: 1018.62037
MathSciNet: MR1962505
Digital Object Identifier: 10.1214/aos/1046294463

Primary: 62G10
Secondary: 62G20

Keywords: Adaptive test , Fisher test , Fisher's quantiles , Goodness-of-fit , linear hypothesis , minimax hypothesis testing , Model selection , nonparametric alternative , Nonparametric regression

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 1 • Februrary 2003
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