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Vitesses maximales de décroissance des erreurs et tests optimaux associés

  • Lucien Birgé
Article

Summary

Under reasonable conditions on Θ, both errors of the tests that the law of a sample of size n belongs to Θ, go to zero like exp[−αn] and exp[− βn]. We shall determine the best possible values for α and β and give a construction of sequences of tests for which the errors decrease with such an optimal rate.

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Références

  1. 0.
    Azencott, R.: Ecole d'Eté de Saint-Flour VIII. Lecture Notes in Mathematics n∘ 774. Berlin-Heidelberg-New York: Springer Verlag 1978Google Scholar
  2. 1.
    Bahadur, R.R.: Stochastic comparison of tests. Ann. Math. Statist. 31, 276–295 (1960)Google Scholar
  3. 2.
    Bahadur, R.R.: Some limit theorems in statistics. Regional conference series in applied mathematics 4. SIAM, J. appl. Math. Philadelphia (1971)Google Scholar
  4. 3.
    Brown, L.D.: Non-local asymptotic optimality of appropriate likelihood ratio tests. Ann. Math. Statist. 42, 1206–1240 (1971)Google Scholar
  5. 4.
    Chernoff, H.: A measure of asymptotic efficiency for tests of a hypothesis based on a sum of observations. Ann. Math. Statist. 23, 493–507 (1952)Google Scholar
  6. 5.
    Dacunha-Castelle, D.: Ecole d'Eté de Probabilités de Saint-Flour VII — Chapitre IX. Lecture Notes in Mathematics n∘ 678. Berlin-Heidelberg-New York: Springer 1977Google Scholar
  7. 6.
    Kullback, S.: Information Theory and Statistics. New York: Dover Publications Inc. 1968Google Scholar
  8. 7.
    Tusnády, G.: On asymptotically optimal tests. Ann. Statist. 5, 385–393 (1977)Google Scholar
  9. 8.
    Tusnády, G.: Testing Statistical Hypothesis (An information theoretic approach). A paraître dans Selecta Statistica CanadianaGoogle Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Lucien Birgé
    • 1
  1. 1.UER de Mathématiques - E.R.A. C.N.R.S. 532Université Paris VIIParis Cedex 05France

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