## The Annals of Statistics

### Adaptive tests of linear hypotheses by model selection

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 31, Number 1 (2003), 225-251.

Dates
First available in Project Euclid: 26 February 2003

https://projecteuclid.org/euclid.aos/1046294463

Digital Object Identifier
doi:10.1214/aos/1046294463

Mathematical Reviews number (MathSciNet)
MR1962505

Zentralblatt MATH identifier
1018.62037

Subjects
Primary: 62G10: Hypothesis testing
Secondary: 62G20: Asymptotic properties

#### Citation

Baraud, Y.; Huet, S.; Laurent, B. Adaptive tests of linear hypotheses by model selection. Ann. Statist. 31 (2003), no. 1, 225--251. doi:10.1214/aos/1046294463. https://projecteuclid.org/euclid.aos/1046294463

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• ECOLE NORMALE SUPERIEURE, DMA 45, RUE D'ULM 75230 PARIS CEDEX 05 FRANCE E-MAIL: yannick.baraud@ens.fr S. HUET
• INRA, LABORATOIRE DE BIOMÉTRIE 78352 JOUY-EN-JOSAS CEDEX FRANCE