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The likelihood ratio criterion and the asymptotic expansion of its distribution

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Summary

Asymptotic expansion of the distribution of the likelihood ratio criterion (LRC) for testing a composite hypothesis is derived under null hypothesis and a correction factor ρ which makes the term of order 1/n in the asymptotic expansion of the distribution of it vanish is obtained. The problem is extended to the case of a general composite hypothesis and of Pitman's local alternatives. The asymptotic distribution of LRC for a simple hypothesis is studied under a fixed alternative.

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Authors
  1. Takesi Hayakawa
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The Institute of Statistical Mathematics

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Hayakawa, T. The likelihood ratio criterion and the asymptotic expansion of its distribution. Ann Inst Stat Math 29, 359–378 (1977). https://doi.org/10.1007/BF02532797

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  • DOI: https://doi.org/10.1007/BF02532797

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