ESAIM: Probability and Statistics, Tome 7 (2003), pp. 147-159.

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 ${ℝ}^{n}$ 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.

DOI : https://doi.org/10.1051/ps:2003006
Classification : 62G10,  62G20
Mots clés : adaptive test, test of monotonicity, test of positivity, qualitative hypothesis testing, nonparametric alternative, nonparametric regression
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Baraud, Yannick; Huet, Sylvie; Laurent, Béatrice. Adaptive tests of qualitative hypotheses. ESAIM: Probability and Statistics, Tome 7 (2003), pp. 147-159. doi : 10.1051/ps:2003006. http://www.numdam.org/articles/10.1051/ps:2003006/

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