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Adaptive tests of qualitative hypotheses

Published online by Cambridge University Press:  15 May 2003

Yannick Baraud
Affiliation:
École Normale Supérieure, DMA, 45 rue d'Ulm, 75230 Paris Cedex 05, France; yannick.baraud@ens.fr.
Sylvie Huet
Affiliation:
Unité BIA, 78352 Jouy-en-Josas Cedex, France; Sylvie.Huet@jouy.inra.fr.
Béatrice Laurent
Affiliation:
bâtiment 425, Université Paris-Sud, 91405 Orsay Cedex, France; beatrice.laurent@math.u-psud.fr.
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Abstract

We propose a test of a qualitative hypothesis on the mean of a n-Gaussian vector. 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 non-asymptotic. For testing positivity or monotonicity, we establish separation rates with respect to the Euclidean distance, over subsets of $\mathbb{R}^{n}$ which are related to Hölderian balls in functional spaces. We provide a simulation study in order to evaluate the procedure when the purpose is to test monotonicity in a functional regression model and to check the robustness of the procedure to non-Gaussian errors.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2003

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References

Baraud, Y., Model selection for regression on a fixed design. Probab. Theory Related Fields 117 (2000) 467-493. CrossRef
Y. Baraud, S. Huet and B. Laurent, Adaptive tests of linear hypotheses by model selection. Ann. Statist. 31 (2003).
Y. Baraud, S. Huet and B. Laurent, Tests for convex hypotheses, Technical Report 2001-66. University of Paris XI, France (2001).
Brunk, H.D., On the estimation of parameters restricted by inequalities. Ann. Math. Statist. 29 (1958) 437-454. CrossRef
Dümbgen, L. and Spokoïny, V.G., Multiscale testing of qualitative hypotheses. Ann. Statist. 29 (2001) 124-152. CrossRef
Ghosal, S., Sen, A. and van der Vaart, A., Testing monotonicity of regression. Ann. Statist. 28 (2000) 1054-1082. CrossRef
Gijbels, I., Hall, P., Jones, M.C. and Koch, I., Tests for monotonicity of a regression mean with guaranteed level. Biometrika 87 (2000) 663-673. CrossRef
Hall, P. and Heckman, N., Testing for monotonicity of a regression mean by calibrating for linear functions. Ann. Statist. 28 (2000) 20-39.
I.A. Ibragimov and R.Z. Has'minskii, Statistical estimation. Asymptotic theory. Springer-Verlag, New York-Berlin, Appl. Math. 16 (1981).
Juditsky, A. and Nemirovski, A., On nonparametric tests of positivity/monotonicity/convexity. Ann. Statist. 30 (2002) 498-527. CrossRef
Laurent, B. and Massart, P., Adaptive estimation of a quadratic functional by model selection. Ann. Statist. 28 (2000) 1302-1338.

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