Journal of Soviet Mathematics

, Volume 52, Issue 2, pp 2955–2964 | Cite as

Estimation of the efficiency of Bol'shev's decision rule in the problem of the distinguishing of two hypotheses

  • M. S. Nikulin
Article
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Abstract

In this communication the efficiency of Bol'shev's optimal decision rule is discussed. The possibility of the use of this rule is considered in the problem of the distinguishing of composite hypotheses in the presence of sufficient statistics.

Keywords

Decision Rule Optimal Decision Composite Hypothesis Optimal Decision Rule 
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Literature cited

  1. 1.
    M. S. Nikulin, “On a result of L. N. Bol'shev from the theory of the statistical testing of hypotheses,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,153, 129–137 (1986).Google Scholar
  2. 2.
    Ya. P. Lumel'skii, “On a method of constructing asymptotically optimal classification tests in the case of a multidimensional normal distribution,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 2, 163–165 (1972).Google Scholar
  3. 3.
    R. A. Abusev and Ya. P. Lumel'skii, “Unbiased estimators and classification problems for multivariate normal populations,” Teor. Veroyatn. Primen.,25, No. 2, 381–389 (1980).Google Scholar
  4. 4.
    L. N. Bol'shev and M. Mirvaliev, “A chi-square goodness-of-fit test for the Poisson, binomial and negative binomial distributions,” Teor. Veroyatn. Primen.,23, No. 3, 481–494 (1978).Google Scholar
  5. 5.
    K. O. Dzhaparidze and M. S. Nikulin, “The probability distributions of the Kolmogorov and omega-squared statistics for continuous distributions with shift and location parameters,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,85, 46–74 (1979).Google Scholar
  6. 6.
    M. S. Nikulin, “The chi-square test for continuous distributions with location and scale parameters,” Teor. Veroyatn. Primen.,18, No. 3, 583–592 (1973).Google Scholar
  7. 7.
    P. Grinvud (P. E. Greenwood) and M. S. Nikulin, “Some remarks with respect to the application of chi-square type tests,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,158, 49–71 (1987).Google Scholar
  8. 8.
    M. S. Nikulin and V. G. Voinov, A chi-square goodness-of-fit test for exponential distributions of the first order. Preprint LOMI E-8-87, Leningrad (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • M. S. Nikulin

There are no affiliations available

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