Analytic bias correction for maximum likelihood estimators when the bias function is non-constant

摘要

Recently, many articles have obtained analytical expressions for the biases of various maximum likelihood estimators, despite their lack of closed-form solution. These bias expressions have provided an attractive alternative to the bootstrap. Unless the bias function is flat, however, the expressions are being evaluated at the wrong point(s). We propose an improved analytical bias-adjusted estimator, in which the bias expression is evaluated at a more appropriate point (at the bias adjusted estimator itself). Simulations illustrate that the improved analytical bias-adjusted estimator can eliminate significantly more bias than the simple estimator, which has been well established in the literature.