An MCMC approach to classical estimation

This paper studies computationally and theoretically attractive estimators called here Laplace type estimators (LTEs), which include means and quantiles of quasi-posterior distributions defined as transformations of general (nonlikelihood-based) statistical criterion functions, such as those in GMM, nonlinear IV, empirical likelihood, and minimum distance methods. The approach generates an alternative to classical extremum estimation and also falls outside the parametric Bayesian approach. For example, it offers a new attractive estimation method for such important semi-parametric problems as censored and instrumental quantile regression, nonlinear GMM and value-at-risk models. The LTEs are computed using Markov Chain Monte Carlo methods, which help circumvent the computational curse of dimensionality. A large sample theory is obtained and illustrated for regular cases.