Bayesian exponentially tilted empirical likelihood
Department of Economics, University of Chicago, 1126 E. 59th Street, Chicago, Illinois 60637, U.S.A. smschenn{at}uchicago.edu
While empirical likelihood has been shown to exhibit many of the properties of conventional parametric likelihoods, a formal probabilistic interpretation has so far been lacking. We show that a likelihood function very closely related to empirical likelihood naturally arises from a nonparametric Bayesian procedure which places a type of noninformative prior on the space of distributions. This prior gives preference to distributions having a small support and, among those sharing the same support, it favours entropy-maximising distributions. The resulting nonparametric Bayesian procedure admits a computationally convenient representation as an empirical-likelihood-type likelihood where the probability weights are obtained via exponential tilting. The proposed methodology provides an attractive alternative to the Bayesian bootstrap as a nonparametric limit of a Bayesian procedure for moment condition models.
Key Words: Empirical likelihood; Entropy; Exponential tilting; Nonparametric Bayesian inference
Received July 2003. Revised June 2004.
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