Abstract
We extend the classical Neyman-Pearson theory for testing composite hypotheses versus composite alternatives, using a convex duality approach, first employed by Witting. Results of Aubin and Ekeland from non-smooth convex analysis are used, along with a theorem of Komlós, in order to establish the existence of a max-min optimal test in considerable generality, and to investigate its properties. The theory is illustrated on representative examples involving Gaussian measures on Euclidean and Wiener space.
Citation
Jaksa Cvitanic. Ioannis Karatzas. "Generalized Neyman-Pearson lemma via convex duality." Bernoulli 7 (1) 79 - 97, February 2001.
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