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Article Dans Une Revue Electronic Journal of Statistics Année : 2015

Hypothesis testing by convex optimization

Résumé

We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated with the hypothesis. With our approach, this problem reduces to testing the hypotheses pairwise. Our central result is a test for a pair of hypotheses of the outlined type which, under appropriate assumptions, is provably nearly optimal. The test is yielded by a solution to a convex programming problem, so that our construction admits computationally efficient implementation. We further demonstrate that our assumptions are satisfied in several important and interesting applications. Finally, we show how our approach can be applied to a rather general detection problem encompassing several classical statistical settings such as detection of abrupt signal changes, cusp detection and multi-sensor detection.

Dates et versions

hal-01335917 , version 1 (22-06-2016)

Identifiants

Citer

Alexander Goldenshluger, Anatoli B. Juditsky, Arkadii S. Nemirovskii. Hypothesis testing by convex optimization . Electronic Journal of Statistics , 2015, 9 (2), pp.1645-1712. ⟨10.1214/15-EJS1054⟩. ⟨hal-01335917⟩
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