Testing composite hypotheses via convex duality

Details Testing composite hypotheses via convex duality Testing composite hypotheses via convex duality

2008-09-24

arxiv.org/abs/0809.4297v2

Bernoulli 2010, Vol. 16, No. 4, 1224-1239

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/10-BEJ249 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ249

We study the problem of testing composite hypotheses versus composite alternatives, using a convex duality approach. In contrast to classical results obtained by Krafft and Witting (Z. Wahrsch. Verw. Gebiete 7 (1967) 289--302), where sufficient optimality conditions are derived via Lagrange duality, we obtain necessary and sufficient optimality conditions via Fenchel duality under compactness assumptions. This approach also differs from the methodology developed in Cvitani\'{c} and Karatzas (Bernoulli 7 (2001) 79--97).

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