Asymptotics for Semiparametric Econometric Models: I. Estimation

Donald Andrews ()

No 908R, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper provides a general framework for proving the square root of T consistency and asymptotic normality of a wide variety of semiparametric estimators. The results apply in time series and cross-sectional modeling contexts. The class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator. The criterion function need not be differentiable. The method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes. This paper also considers tests of nonlinear parametric restrictions in seimparametric econometric models. To date, only Wald tests of such restrictions have been considered in the literature. Here, Wald, Lagrange multiplier, and likelihood ratio-like tests statistics are considered. A general framework is provided for proving that these test statistics have asymptotic chi-square distributions under the null hypothesis and local alternatives. The results hold for a wide variety of underlying estimation techniques and in a wide variety of model scenarios.

Keywords: Asymptotic normality; empirical process; infinite dimensional nuisance parameter; Lagrange multiplier test; likelihood ratio-like test; nonparametric estimation; semiparametric estimation; semiparametric model; semiparametric test; stochastic equicontinuity; Wald test; weak convergence (search for similar items in EconPapers)
Pages: 100 pages
Date: 1989, Revised 1990-08
Note: CFP 863.
References: Add references at CitEc
Citations: View citations in EconPapers (10)

Published in Econometrica (January 1994), 62(1): 43-72

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