The Annals of Statistics

Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function

Yannick Baraud, Sylvie Huet, and Béatrice Laurent

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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.

Article information

Source
Ann. Statist., Volume 33, Number 1 (2005), 214-257.

Dates
First available in Project Euclid: 8 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1112967705

Digital Object Identifier
doi:10.1214/009053604000000896

Mathematical Reviews number (MathSciNet)
MR2157802

Zentralblatt MATH identifier
1065.62109

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

Keywords
Tests of qualitative hypotheses nonparametric test test of positivity test of monotonicity test of convexity rate of testing Gaussian regression

Citation

Baraud, Yannick; Huet, Sylvie; Laurent, Béatrice. Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function. Ann. Statist. 33 (2005), no. 1, 214--257. doi:10.1214/009053604000000896. https://projecteuclid.org/euclid.aos/1112967705


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References

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