Open Access
November 2010 Testing composite hypotheses via convex duality
Birgit Rudloff, Ioannis Karatzas
Bernoulli 16(4): 1224-1239 (November 2010). DOI: 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 Cvitanić and Karatzas (Bernoulli 7 (2001) 79–97).


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Birgit Rudloff. Ioannis Karatzas. "Testing composite hypotheses via convex duality." Bernoulli 16 (4) 1224 - 1239, November 2010.


Published: November 2010
First available in Project Euclid: 18 November 2010

zbMATH: 1207.62101
MathSciNet: MR2759177
Digital Object Identifier: 10.3150/10-BEJ249

Keywords: composite hypotheses , convex duality , generalized Neyman–Pearson lemma , randomized test

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

Vol.16 • No. 4 • November 2010
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