Bernoulli

  • Bernoulli
  • Volume 16, Number 4 (2010), 1224-1239.

Testing composite hypotheses via convex duality

Birgit Rudloff and Ioannis Karatzas

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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 Cvitanić and Karatzas (Bernoulli 7 (2001) 79–97).

Article information

Source
Bernoulli Volume 16, Number 4 (2010), 1224-1239.

Dates
First available in Project Euclid: 18 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1290092904

Digital Object Identifier
doi:10.3150/10-BEJ249

Mathematical Reviews number (MathSciNet)
MR2759177

Zentralblatt MATH identifier
1207.62101

Keywords
composite hypotheses convex duality generalized Neyman–Pearson lemma randomized test

Citation

Rudloff, Birgit; Karatzas, Ioannis. Testing composite hypotheses via convex duality. Bernoulli 16 (2010), no. 4, 1224--1239. doi:10.3150/10-BEJ249. https://projecteuclid.org/euclid.bj/1290092904.


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