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Bias Reduction for Bayesian and Frequentist Estimators

45 Pages Posted: 6 Nov 2006  

Alan Bester

University of Chicago Graduate School of Business

Christian Hansen

University of Chicago - Booth School of Business - Econometrics and Statistics

Date Written: December 22, 2005

Abstract

We show that in parametric likelihood models the first order bias in the posterior mode and the posterior mean can be removed using objective Bayesian priors. These bias-reducing priors are defined as the solution to a set of differential equations which may not be available in closed form. We provide a simple and tractable data dependent prior that solves the differential equations asymptotically and removes the first order bias. When we consider the posterior mode, this approach can be interpreted as penalized maximum likelihood in a frequentist setting. We illustrate the construction and use of the bias-reducing priors in simple examples and a simulation study.

Keywords: Bias, Objective Bayes, Penalized likelihood

JEL Classification: C11, C13

Suggested Citation

Bester, Alan and Hansen, Christian, Bias Reduction for Bayesian and Frequentist Estimators (December 22, 2005). Available at SSRN: https://ssrn.com/abstract=942803 or http://dx.doi.org/10.2139/ssrn.942803

Alan Bester (Contact Author)

University of Chicago Graduate School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-834-1714 (Phone)

Christian Hansen

University of Chicago - Booth School of Business - Econometrics and Statistics ( email )

Chicago, IL 60637
United States
773-834-1702 (Phone)

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