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test of positivity

ESAIM: Probability and Statistics (1)

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Adaptive tests of qualitative hypotheses
Yannick Baraud, Sylvie Huet, Béatrice Laurent
Journal:

ESAIM: Probability and Statistics / Volume 7 / March 2003

Published online by Cambridge University Press:

15 May 2003, pp. 147-159

Print publication:

March 2003
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We propose a test of a qualitative hypothesis on the mean of a n-Gaussianvector. The testing procedure is available when the variance of theobservations is unknown and does not depend on any prior information onthe alternative. The properties of the test are non-asymptotic. Fortesting positivity or monotonicity, weestablish separation rates with respect to the Euclidean distance, oversubsets of $\mathbb{R}^{n}$ which are related to Hölderian balls in functionalspaces. We provide a simulation study in order to evaluate theprocedure when the purpose is to test monotonicity in a functionalregression model and to check the robustness of the procedure tonon-Gaussian errors.