Analytical and Bootstrap Bias Corrections

Abstract

Maximum likelihood estimators are usually biased: In finite samples, their expected value differs from the true parameter value. This is a systematic error. It typically vanishes as the sample size increases, but it can be large in small samples. Different strategies can be employed to reduce such systematic error. In this chapter, we present two analytical bias corrections. We also show how the bootstrap can be used to bias-correct estimators. Bias corrections in different statistical models are presented and discussed. In particular, we address the issue of bias-correcting covariance matrix estimators in heteroskedastic linear regressions.