Efficient Simulation-Based Minimum Distance Estimation and Indirect Inference

TL;DR

This paper introduces a simulation-based minimum distance estimation method using indirect inference with nonparametric density estimators, achieving asymptotic normality and efficiency at the Cramer-Rao bound.

Contribution

It develops a new estimation approach that combines simulation, nonparametric density estimation, and indirect inference to attain optimal asymptotic properties.

Findings

Estimators are asymptotically normal.

Variance matches the Cramer-Rao bound.

Method is applicable under mild assumptions.

Abstract

Given a random sample from a parametric model, we show how indirect inference estimators based on appropriate nonparametric density estimators (i.e., simulation-based minimum distance estimators) can be constructed that, under mild assumptions, are asymptotically normal with variance-covarince matrix equal to the Cramer-Rao bound.