  This paper studies computationally and theoretically attractive estimators
called the Laplace type estimators (LTE), which include means and quantiles of
Quasi-posterior distributions defined as transformations of general
(non-likelihood-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, nonlinear GMM and value-at-risk models. The
LTE's are computed using Markov Chain Monte Carlo methods, which help
circumvent the computational curse of dimensionality. A large sample theory is
obtained for regular cases.
