Discussion of “Hypotheses testing by convex optimization”
نویسندگان
چکیده
منابع مشابه
Discussion of “ Hypotheses testing by convex optimization ” ∗
We congratulate the authors on a stimulating paper on a very intuitive and general approach to construct hypotheses tests. Restricting the considered class of tests to simple ones determined by a detector function φ, it seems most natural to minimize over φ and maximize over the pair (x, y) ∈ X ×Y where X is the hypothesis and Y the alternative. Particularly, this guarantees that the correspond...
متن کاملOn Sequential Hypotheses Testing via Convex Optimization
We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [1]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector of parameters underlying the distribution of observations belongs to a convex set. The nearly optimal under appropriate conditions test is yielded by a solutio...
متن کاملHypothesis testing by convex optimization
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 optima...
متن کاملRejoinder of “ Hypothesis testing by convex optimization ” ∗
First of all, we would like to thank all the discussants for their interesting, thought–provoking comments and thorough investigation. We also thank the editors for the opportunity to comment briefly on a few issues raised in the discussions. The comments of the discussants underline importance of the topic discussed in our paper, namely, that of application of convex optimization methodology t...
متن کاملTesting Composite Hypotheses via Convex Duality ∗
We study the problem of testing composite hypotheses versus composite alternatives, using a convex duality approach. In contrast to classical results obtained by Krafft & Witting [11], where sufficient optimality conditions are obtained via Lagrange duality, we obtain necessary and sufficient optimality conditions via Fenchel duality under some compactness assumptions. This approach also differ...
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ژورنال
عنوان ژورنال: Electronic Journal of Statistics
سال: 2015
ISSN: 1935-7524
DOI: 10.1214/15-ejs1014