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

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.