Bernoulli

Generalized Neyman-Pearson lemma via convex duality

Jaksa Cvitanic and Ioannis Karatzas

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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.

Article information

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

Dates
First available in Project Euclid: 29 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1080572340

Mathematical Reviews number (MathSciNet)
MR1811745

Zentralblatt MATH identifier
1054.62056

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

Citation

Cvitanic, Jaksa; Karatzas, Ioannis. Generalized Neyman-Pearson lemma via convex duality. Bernoulli 7 (2001), no. 1, 79--97. https://projecteuclid.org/euclid.bj/1080572340


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References

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