Implementation of Estimating Function-Based Inference Procedures With Markov Chain Monte Carlo Samplers
Lü Tian, Jun S. Liu, Lee‐Jen Wei · Journal of the American Statistical Association · 2007
Under a semiparametric or nonparametric setting, inferences about the unknown parameter are often made based on a nonsmooth estimating function. Resampling methods are quite handy for obtaining good approximations to the distribution of the consistent estimator when the estimating equation and its resampled counterparts are not difficult to solve numerically. In this article we propose a simple, flexible procedure that provides such approximations through the standard Markov chain Monte Carlo sampler without solving any equations. More generally, the procedure may locate all possible roots of the estimating equation and provides an approximation to the distribution of each root. We illustrate our proposed procedure extensively with three examples and evaluate its performance comprehensively through a simulation study.