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Full-Text Articles in Social and Behavioral Sciences
An Empirical Process Central Limit Theorem For Dependent Non-Identically Distributed Random Variables, Donald W.K. Andrews
An Empirical Process Central Limit Theorem For Dependent Non-Identically Distributed Random Variables, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper establishes a central limit theorem (CLT) for empirical processes indexed by smooth functions. The underlying random variables may be temporally dependent and non-identically distributed. In particular, the CLT holds for near epoch dependent (i.e., functions of mixing processes) triangular arrays, which include strong mixing arrays, among others. The results apply to classes of functions that have series expansions. The proof of the CLT is particularly simple; no chaining argument is required. The results can be used to establish the asymptotic normality of semiparametric estimators in time series contexts. An example is provided.
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 …