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Bayesian exponentially tilted empirical likelihood

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  • Susanne M. Schennach

Abstract

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. Copyright 2005, Oxford University Press.

Suggested Citation

  • Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
  • Handle: RePEc:oup:biomet:v:92:y:2005:i:1:p:31-46
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    File URL: http://hdl.handle.net/10.1093/biomet/92.1.31
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