The Comparisons of Approximations for Log-Likelihood Ratio Statistics in Normal Population

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  • 正規分布の検定における対数尤度比統計量の近似に関する比較研究
  • セイキ ブンプ ノ ケンテイ ニ オケル タイスウ ユウドヒ トウケイリョウ

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Recently, Arizono et al. have derived the cumulant generating function for the log-likelihood ratio statistics under any alternative hypothesis. Further, they have proposed two approximations for the log-likelihood ratio statistics by using only the first and the second cumulants. As a result, these approximations have the high accuracy under the null hypothesis. In addition, it is known that there is some room for further improvement for accuracy of them under the alternative hypothesis. In this paper, we consider the approximations of the log-likelihood ratio statistics by using the higher order cumulants. Then, we compare some approximations for the log-likelihood ratio statistics.

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