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 |

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Category: | math |

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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 |

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Date available: | 2009-09-24T19:26:02Z |

Last updated: | 2015-03-27 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/135290 |

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Reference: | [2] Bucklew I. A.: Large Deviation Techniques in Decision, Simulation and Estimatio. |

Reference: | [3] Chernoff H.: A measure of asymptotic efficiency for tests of hypothesis based on the sum of observation. |

Reference: | [4] Chernoff H.: Large sample theory: Parametric cas. |

Reference: | [6] Krafft O., Plachky D.: Bounds for the power of likelihood ratio tests and their asymptotic and their asymptotic propertie. |

Reference: | [7] Krafft O., Puri M. L.: The asymptotic behaviour of the minimax risk for multiple decision problem. |

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 |

Reference: | [9] Liese F., Vajda I.: Convex Statistical Distance. |

Reference: | [10] Rüschendorf L.: Asymptotische Statisti. |

Reference: | [11] Rukhin A. L.: Adaptive procedure for a finite numbers of probability distributions.Statist. Decis. Theory Related Topics III. 2 (1982), 269–285 MR 0705319 |

Reference: | [12] Rukhin A. L.: Adaptive classification procedure. |

Reference: | [13] Rukhin A. L.: Adaptive testing of multiple hypotheses for stochastic processe. |

Reference: | [14] Rukhin A. L., Vajda I.: Adaptive decision making for stochastic processe. |

Reference: | [15] Vajda I.: Theory of Statistical Inference and Informatio. |

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