Asymptotics for Semiparametric Econometric Models: III. Testing and Examples
Abstract
This paper considers tests of nonlinear parametric restrictions in semiparametric econometric models. To date, only Wald tests of such restrictions have been considered in the literature. Here, Wald, Lagrange multiplier, and likelihood ratio-like test statistics are considered and are shown to have asymptotic chi-square distributions under the null and local alternatives. The results hold for a wide variety of underlying estimation techniques and in a wide variety of model scenarios. A number of examples are given to illustrate the testing results of this paper and the estimation and stochastic equicontinuity results of the antecedents to this paper, viz. Andrews (1989b, c).
JEL Classification: 211
Keywords: Lagrange multiplier test, likelihood ratio test, semiparametric model, semiparametric tests, Wald test, asymptotic theory