Posterior expectation based on empirical likelihoods

Posterior expectation is widely used as a Bayesian point estimator. In this note we extend it from parametric models to nonparametric models using empirical likelihood, and develop a nonparametric analogue of James-Stein estimation. We use the Laplace method to establish asymptotic approximations to our proposed posterior expectations, and show by simulation that they are often more efficient than the corresponding classical nonparametric procedures, especially when the underlying data are skewed.