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The misclassification error of the maximum likelihood procedure when deciding among a finite choice of distributions

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Abstract

Suppose we have a sample randomly drawn from one of a given number of distributions. We wish to select the distribution based on the optimal maximum likelihood procedure. In this note, various tight estimates are derived under general conditions for the probability of making the wrong selection. The estimates are also extended to the case of many exponential families, where the general conditions fail. Some of the estimates are illustrated by means of simulation. The practical use of the estimates is discussed.

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References

  • Blackwell D, Hodges JL (1959) The probability in the extreme tail of a convolution. Ann Math Stat 31: 1113–1120

    Article  MathSciNet  Google Scholar 

  • Chernoff H (1952) A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann Math Stat 23: 493–507

    Article  MATH  MathSciNet  Google Scholar 

  • Daniels HE (1954) Saddlepoint approximations in statistics. Ann Math Stat 25: 631–650

    Article  MATH  MathSciNet  Google Scholar 

  • Groeneboom P, Oosterhoff J, Ruymgaart FH (1979) Large deviation theorems for empirical probability measures. Ann Prob 7: 553–586

    Article  MATH  MathSciNet  Google Scholar 

  • Johnson NL, Kotz S, Kemp AW (1992) Univariate discrete distributions, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distributions, vol 1, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Johnson NL, Kotz S, Balakrishnan N (1995) Continuous univariate distributions, vol 2, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Lugannani R, Rice S (1980) Saddle point approximation for the distribution of the sum of independent random variables. Adv Appl Prob 12: 475–490

    Article  MATH  MathSciNet  Google Scholar 

  • Withers CS, Nadarajah S (2008a) Power of a class of goodness-of-fit test I. ESIAM: Prob Stat. doi:10.1051/ps:2008013

  • Withers CS, Nadarajah S (2008b) Tilted edgeworth expansions for asymptotically normal vectors. Ann Inst Stat Math. doi:10.1007/s10463-008-0206-0

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Authors and Affiliations

  1. Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand

    Christopher S. Withers

  2. School of Mathematics, University of Manchester, Manchester, M13 9PL, UK

    Saralees Nadarajah

Authors
  1. Christopher S. Withers
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  2. Saralees Nadarajah
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Correspondence to Saralees Nadarajah.

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Withers, C.S., Nadarajah, S. The misclassification error of the maximum likelihood procedure when deciding among a finite choice of distributions. Metrika 72, 233–250 (2010). https://doi.org/10.1007/s00184-009-0250-7

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  • DOI: https://doi.org/10.1007/s00184-009-0250-7

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