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On parameter transformations and interval estimation. (English) Zbl 0566.62022
Parameterizations which reduce the asymptotic bias and skewness of various pivotal quantities arising in large-sample theory are discussed for models depending on an unknown scalar parameter. Transformation formulae by which such parameterizations can be obtained are derived, and these formulae extend those for one-dimensional curved exponential families given by {\it P. Hougaard}, J. R. Stat. Soc., Ser. B 44, 244-252 (1982; Zbl 0494.62032). To assess the accuracy of normal approximations to the distributions of the pivots, their second-order properties are considered and comparisons with the signed square root of the likelihood-ratio statistic are drawn.

MSC:
62F12Asymptotic properties of parametric estimators
62E20Asymptotic distribution theory in statistics
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