On bootstrap and analytical bias corrections

Abstract

This paper explores the relationship between bias correction of maximum likelihood estimators through bootstrap and analytical series expansions. It shows that the bootstrap provides a natural way of defining finite sample bias-corrected maximum likelihood estimators in one-parameter models. Bootstrap-corrected estimators for multiparameter models are obtained. Simulation results comparing the finite-sample performance of bias-corrected maximum likelihood estimators based on the bootstrap and on analytical series expansions are also given.