RELIABLE INFERENCE FROM EMPIRICAL LIKELIHOODS

 

S. A. Corcoran and A. C. Davison

Department of Statistics, Oxford University

and

R. H. Spady

Nuffield College, Oxford University

 

March 24 1995

 

Abstract

Theoretical work has shown that similar asymptotic theory applies to empirical likelihood and parametric likelihood, and in particular that the higher-order properties of the empirical likelihood ratio statistic can be improved by Bartlett adjustment. We use simulation to show that for small and moderate samples the adjusted statistic performs worse than a related statistic that does not have the same 'good' higher-order behaviour. The general conclusion is that standard asymptotic calculations are not useful in understanding the small-sample behaviour of nonparametric likelihood statistics