Second and Third Order Bias Reduction for One-Parameter Family Models

Abstract

In this paper we derive second and third order bias-corrected maximum likelihood estimates in general uniparametric models. We compare the corrected estimates and the usual maximum likelihood estimate in terms of their mean squared errors. We also obtain closed-form expressions for bias-corrected estimates in one-parameter exponential family models. Our results cover many important and commonly used distributions.Asymptotic expansion; bias correction, exponential family; maximum likelihood estimate