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2015 Hypothesis testing by convex optimization
Alexander Goldenshluger, Anatoli Juditsky, Arkadi Nemirovski
Electron. J. Statist. 9(2): 1645-1712 (2015). DOI: 10.1214/15-EJS1054


We discuss a general approach to hypothesis testing. The main “building block” of the proposed construction is a test for a pair of hypotheses in the situation where each particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated with the hypothesis. This test, under appropriate assumptions, is nearly optimal and is yielded by a solution to a convex optimization problem, so that the 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 testing problems encompassing several classical statistical settings.


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Alexander Goldenshluger. Anatoli Juditsky. Arkadi Nemirovski. "Hypothesis testing by convex optimization." Electron. J. Statist. 9 (2) 1645 - 1712, 2015.


Received: 1 September 2014; Published: 2015
First available in Project Euclid: 7 August 2015

zbMATH: 1327.62287
MathSciNet: MR3379005
Digital Object Identifier: 10.1214/15-EJS1054

Primary: 62C20, 62G10
Secondary: 62M02, 62M10, 65K10, 90C25

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.9 • No. 2 • 2015
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