Estimation of non‐smooth non‐parametric estimating equations models with dependent data

Abstract

This article considers estimation of non‐smooth possibly overidentified non‐parametric estimating equations models with weakly dependent data. The estimators are based on a kernel smoothed version of the generalized empirical likelihood and the generalized method of moments approaches. The article derives the asymptotic normality of both estimators and shows that the proposed local generalized empirical likelihood estimator is more efficient than the local generalized moment estimator unless a two‐step procedure is used. The article also proposes novel tests for the correct specification of the considered model that are shown to have power against local alternatives and are consistent against fixed alternatives. Monte Carlo simulations and an empirical application illustrate the finite sample properties and applicability of the proposed estimators and test statistics.