Reduction of bias and skewness with applications to second order accuracy |
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Authors: | Christopher S Withers Saralees Nadarajah |
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Institution: | 1.Applied Mathematics Group, Industrial Research Limited,Lower Hutt,New Zealand;2.School of Mathematics,University of Manchester,Manchester,UK |
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Abstract: | Suppose ^(q)]{\widehat{\theta}} is an estimator of θ in
\mathbbR{\mathbb{R}} that satisfies the central limit theorem. In general, inferences on θ are based on the central limit approximation. These have error O(n
−1/2), where n is the sample size. Many unsuccessful attempts have been made at finding transformations which reduce this error to O(n
−1). The variance stabilizing transformation fails to achieve this. We give alternative transformations that have bias O(n
−2), and skewness O(n
−3). Examples include the binomial, Poisson, chi-square and hypergeometric distributions. |
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Keywords: | |
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