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February 2005 Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function
Yannick Baraud, Sylvie Huet, Béatrice Laurent
Ann. Statist. 33(1): 214-257 (February 2005). DOI: 10.1214/009053604000000896

Abstract

In this paper we propose a general methodology, based on multiple testing, for testing that the mean of a Gaussian vector in ℝn belongs to a convex set. We show that the test achieves its nominal level, and characterize a class of vectors over which the tests achieve a prescribed power. In the functional regression model this general methodology is applied to test some qualitative hypotheses on the regression function. For example, we test that the regression function is positive, increasing, convex, or more generally, satisfies a differential inequality. Uniform separation rates over classes of smooth functions are established and a comparison with other results in the literature is provided. A simulation study evaluates some of the procedures for testing monotonicity.

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Yannick Baraud. Sylvie Huet. Béatrice Laurent. "Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function." Ann. Statist. 33 (1) 214 - 257, February 2005. https://doi.org/10.1214/009053604000000896

Information

Published: February 2005
First available in Project Euclid: 8 April 2005

zbMATH: 1065.62109
MathSciNet: MR2157802
Digital Object Identifier: 10.1214/009053604000000896

Subjects:
Primary: 62G10
Secondary: 62G20

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 1 • February 2005
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