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On Parameter Transformations and Interval Estimation

T. J. DiCiccio
Biometrika
Vol. 71, No. 3 (Dec., 1984), pp. 477-485
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2336556
Stable URL: http://www.jstor.org/stable/2336556
Page Count: 9
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On Parameter Transformations and Interval Estimation
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Abstract

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 Hougaard (1982). 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.

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