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

By Y. Baraud, Sylvie Huet, Béatrice Laurent. 2005

55 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cea7aefdcc6d8787b681b4a9849fb612a357d8a4

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In Statistics and Probability

Citations in the corpus

TESTING REGRESSION MONOTONICITY IN ECONOMETRIC MODELS (2012, background): “The list of other papers includes Schlee (1982), Bowman, Jones, and Gijbels (1998), Dumbgen and Spokoiny (2001), Durot (2003), Beraud, Huet, and Laurent (2005), and Wang and Meyer (2011).”
TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES (2013, background): “See, for example, Dümbgen and Spokoiny (2001), Juditsky and Nemirovski (2002) and Baraud, Huet, and Laurent (2005) among others.”
Minimax Testing of a Composite null Hypothesis Defined via a Quadratic Functional in the Model of regression (2012, background): “More recently, the nonasymptotic approach to the minimax testing gained popularity (Baraud et al., 2003, 2005, Laurent et al., 2011, 2012).”