Testing composite hypotheses via convex duality
arXiv:0809.4297 · doi:10.3150/10-BEJ249
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 CvitaniÄ and Karatzas (Bernoulli 7 (2001) 79--97).
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)