Generalized Neyman-Pearson lemma via convex duality

Jaksa Cvitanic and Ioannis Karatzas

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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.

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Bernoulli, Volume 7, Number 1 (2001), 79-97.

First available in Project Euclid: 29 March 2004

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hypothesis testing Komlós theorem non-smooth convex analysis normal cones optimal generalized tests saddle-points stochastic games subdifferentials


Cvitanic, Jaksa; Karatzas, Ioannis. Generalized Neyman-Pearson lemma via convex duality. Bernoulli 7 (2001), no. 1, 79--97.

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