Exponential rates for the error probabilities in selection procedures

Friedrich Liese; Klaus J. Miescke

Kybernetika (1999)

  • Volume: 35, Issue: 3, page [309]-332
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Liese, Friedrich, and Miescke, Klaus J.. "Exponential rates for the error probabilities in selection procedures." Kybernetika 35.3 (1999): [309]-332. <http://eudml.org/doc/33430>.

@article{Liese1999,
abstract = {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.},
author = {Liese, Friedrich, Miescke, Klaus J.},
journal = {Kybernetika},
keywords = {generating functions of likelihood ratio; exponential family; generating functions of likelihood ratio; exponential family},
language = {eng},
number = {3},
pages = {[309]-332},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Exponential rates for the error probabilities in selection procedures},
url = {http://eudml.org/doc/33430},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Liese, Friedrich
AU - Miescke, Klaus J.
TI - Exponential rates for the error probabilities in selection procedures
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 3
SP - [309]
EP - 332
AB - 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.
LA - eng
KW - generating functions of likelihood ratio; exponential family; generating functions of likelihood ratio; exponential family
UR - http://eudml.org/doc/33430
ER -

References

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  1. Bucklew I. A., Large Deviation Techniques in Decision, Simulation and Estimatio 
  2. Chernoff H., A measure of asymptotic efficiency for tests of hypothesis based on the sum of observation 
  3. Chernoff H., Large sample theory: Parametric cas 
  4. Krafft O., Plachky D., Bounds for the power of likelihood ratio tests and their asymptotic and their asymptotic propertie 
  5. Krafft O., Puri M. L., The asymptotic behaviour of the minimax risk for multiple decision problem 
  6. Liese F., Miescke K. L., Exponential Rates for the Error Probabilities in Selection Procedures, Preprint 96/5, FB Mathematik, Universität Rostock, Rostock 1996 MR1704669
  7. Liese F., Vajda I., Convex Statistical Distance 
  8. Rüschendorf L., Asymptotische Statisti 
  9. Rukhin A. L., Adaptive procedure for a finite numbers of probability distributions, Statist. Decis. Theory Related Topics III. 2 (1982), 269–285 (1982) MR0705319
  10. Rukhin A. L., Adaptive classification procedure 
  11. Rukhin A. L., Adaptive testing of multiple hypotheses for stochastic processe 
  12. Rukhin A. L., Vajda I., Adaptive decision making for stochastic processe 
  13. Vajda I., Theory of Statistical Inference and Informatio 

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