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Title: Exponential rates for the error probabilities in selection procedures (English)
Author: Liese, Friedrich
Author: Miescke, Klaus J.
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 35
Issue: 3
Year: 1999
Pages: [309]-332
Summary lang: English
Category: math
Summary: For a sequence of statistical experiments with a finite parameter set the asymptotic behavior of the maximum risk is studied for the problem of classification into disjoint subsets. The exponential rates of the optimal decision rule is determined and expressed in terms of the normalized limit of moment generating functions of likelihood ratios. Necessary and sufficient conditions for the existence of adaptive classification rules in the sense of Rukhin [Ru1] are given. The results are applied to the problem of the selection of the best population. Exponential families are studied as a special case, and an example for the normal case is included. (English)
Keyword: generating functions of likelihood ratio
Keyword: exponential family
MSC: 62C25
MSC: 62F07
MSC: 62H30
idZBL: Zbl 1274.62158
idMR: MR1704669
Date available: 2009-09-24T19:26:02Z
Last updated: 2015-03-27
Stable URL:
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Reference: [3] Chernoff H.: A measure of asymptotic efficiency for tests of hypothesis based on the sum of observation.
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Reference: [8] Liese F., Miescke K. L.: Exponential Rates for the Error Probabilities in Selection Procedures.Preprint 96/5, FB Mathematik, Universität Rostock, Rostock 1996 MR 1704669
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Reference: [12] Rukhin A. L.: Adaptive classification procedure.
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Reference: [15] Vajda I.: Theory of Statistical Inference and Informatio.


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