Smooth Minimum Distance Estimation and Testing with Conditional Estimating Equations: Uniform in Bandwidth Theory

Abstract

We study the influence of a bandwidth parameter in inference with conditional estimating equations. In that aim, we propose a new class of smooth minimum distance estimators and we develop a theory that focuses on uniformity in bandwidth. We establish a vn-asymptotic representation of our estimator as a process indexed by a bandwidth that can vary within a wide range including bandwidths independent of the sample size. We develop an efficient version of our estimator. We also study its behavior in misspecified models. We develop a procedure based on a distance metric statistic for testing restrictions on parameters as well as a bootstrap technique to account for the bandwidth’s influence. Our new methods are simple to implement, apply to non-smooth problems, and perform well in our simulations.

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Replaces

Pascal Lavergne, and Valentin Patilea, “Smooth Minimum Distance Estimation and Testing with Conditional Estimating Equations: Uniform in Bandwidth Theory”, TSE Working Paper, n. 13-404, March 2013.

Reference

Pascal Lavergne, and Valentin Patilea, “Smooth Minimum Distance Estimation and Testing with Conditional Estimating Equations: Uniform in Bandwidth Theory”, Journal of Econometrics, vol. 177, n. 1, November 2013, pp. 47–59.