Testing composite hypotheses via convex duality
Probability
2010-11-29 v2 Optimization and Control
Statistics Theory
Statistics Theory
Abstract
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).
Keywords
Cite
@article{arxiv.0809.4297,
title = {Testing composite hypotheses via convex duality},
author = {Birgit Rudloff and Ioannis Karatzas},
journal= {arXiv preprint arXiv:0809.4297},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.3150/10-BEJ249 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)