Reduction of bias and skewness with applications to second order accuracy

摘要

Suppose θ is an estimator of θ in R that satisfies the central limit theorem. In general, inferences on 6 are based on the central limit approximation. These have error 0(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 0(n~(-3)). Examples include the binomial, Poisson, chi-square and hypergeometric distributions.