ASYMPTOTIC BAYESIAN-ANALYSIS BASED ON A LIMITED INFORMATION ESTIMATOR

We study asymptotic Bayesian analysis based on a limited information e stimator, with an unknown partial likelihood function. It is found tha t the asymptotic distribution of the estimator approximates the poster ior distribution, provided that the estimator's distribution converges uniformly in local neigborhoods around the true parameter value. This provides a Bayesian interpretation to classical limited information p rocedures, making them available for a semi-parametric Bayesian analys is. Uniform convergence in distribution is essential for such result, as illustrated by examples in which the estimators are pointwise asymp totically normal at every parameter value, but the posterior distribut ions display discontinuous and possibly non-normal behaviors. (C) 1999 Elsevier Science S.A. All rights reserved.