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Asymptotics For Semiparametric Econometric Models: Iii. Testing And Examples, Donald W.K. Andrews
Asymptotics For Semiparametric Econometric Models: Iii. Testing And Examples, Donald W.K. Andrews
Cowles Foundation Discussion Papers
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, …
Asymptotics For Semiparametric Econometric Models: I. Estimation, Donald W.K. Andrews
Asymptotics For Semiparametric Econometric Models: I. Estimation, Donald W.K. Andrews
Cowles Foundation Discussion Papers
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 …