Testing composite hypotheses via convex duality

Birgit Rudloff; Ioannis Karatzas

doi:10.3150/10-BEJ249

Testing composite hypotheses via convex duality

Birgit Rudloff, Ioannis Karatzas

Institute for Statistics and Mathematics

Publication: Scientific journal › Journal article › peer-review

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

Original language	English
Pages (from-to)	1224 - 1239
Journal	Bernoulli
Volume	16
Issue number	4
DOIs	https://doi.org/10.3150/10-BEJ249
Publication status	Published - 2010

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@article{1706b786f10b4d429878bfa8f5f0af0e,

title = "Testing composite hypotheses via convex duality",

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 Cvitanic{\' } and Karatzas (Bernoulli 7 (2001) 79–97).",

author = "Birgit Rudloff and Ioannis Karatzas",

year = "2010",

doi = "10.3150/10-BEJ249",

language = "English",

volume = "16",

pages = "1224 -- 1239",

journal = "Bernoulli",

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publisher = "Bernoulli Society for Mathematical Statistics and Probability",

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T1 - Testing composite hypotheses via convex duality

AU - Rudloff, Birgit

AU - Karatzas, Ioannis

PY - 2010

Y1 - 2010

N2 - 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 Cvitanic ́ and Karatzas (Bernoulli 7 (2001) 79–97).

AB - 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 Cvitanic ́ and Karatzas (Bernoulli 7 (2001) 79–97).

UR - http://www.princeton.edu/~brudloff/RudloffKaratzas10.pdf

U2 - 10.3150/10-BEJ249

DO - 10.3150/10-BEJ249

M3 - Journal article

SN - 1350-7265

VL - 16

SP - 1224

EP - 1239

JO - Bernoulli

JF - Bernoulli

IS - 4

ER -

Testing composite hypotheses via convex duality

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