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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: Ii. Stochastic Equicontinuity And Nonparametric Kernel Estimation, Donald W.K. Andrews
Asymptotics For Semiparametric Econometric Models: Ii. Stochastic Equicontinuity And Nonparametric Kernel Estimation, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper presents several stochastic equicontinuity results that are useful for establishing the asymptotic properties of estimators and tests in parametric, semiparametric, and nonparametric econometric models. In particular, they can be applied straightforwardly in the estimation and testing results of Andrews (1989b). The paper takes various stochastic equicontinuity results from the probability literature, which rely on entropy conditions of one sort or another, and provides primitive conditions under which the entropy conditions hold. This yields stochastic equicontinuity results that are readily applicable in a variety of contexts. This paper also presents a number of consistency results for nonparametric kernel estimators …