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On standardizing the signed root log likelihood ratio statistic. (English) Zbl 1335.62089

Summary: A simple connection between the Bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant of the \(p^{\ast }\) formula – an approximate conditional density for the maximum likelihood estimate given an exact or an approximate ancillary statistic – was established in [O. E. Barndorff-Nielsen and D. R. Cox, J. R. Stat. Soc., Ser. B 46, 483–495 (1984; Zbl 0581.62016)]. In this paper, the explicit form of the normalizing constant of the \(p^{\ast }\) formula for the scalar parameter model is derived. By change of variables, the mean and variance of the signed root log likelihood ratio statistic are obtained explicitly, and, hence, tail probabilities can be calculated from the standardized signed root log likelihood ratio statistic. Examples are used to illustrate the implementation and accuracy of the proposed method.

MSC:

62H10 Multivariate distribution of statistics
62E20 Asymptotic distribution theory in statistics
62F10 Point estimation

Citations:

Zbl 0581.62016
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References:

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