Non-Parametric Maximum Likelihood Density Estimation and Simulation-Based Minimum Distance Estimators

TL;DR

This paper establishes the asymptotic normality of indirect inference estimators that utilize non-parametric maximum likelihood density estimators, providing theoretical guarantees and variance characterizations.

Contribution

It introduces asymptotic normality results for simulation-based minimum distance estimators using non-parametric MLE densities, with variance matching Fisher information under correct model specification.

Findings

Asymptotic normality of the estimators is proven.

Variance equals the inverse Fisher information when the model is correct.

Uniform convergence rates and a Donsker-type theorem are established.

Abstract

Indirect inference estimators (i.e., simulation-based minimum distance estimators) in a parametric model that are based on auxiliary non-parametric maximum likelihood density estimators are shown to be asymptotically normal. If the parametric model is correctly specified, it is furthermore shown that the asymptotic variance-covariance matrix equals the inverse of the Fisher-information matrix. These results are based on uniform-in-parameters convergence rates and a uniform-in-parameters Donsker-type theorem for non-parametric maximum likelihood density estimators.