Title

An Empirical Process Central Limit Theorem for Dependent Non-Identically Distributed Random Variables

Document Type

Discussion Paper

Publication Date

5-1-1989

CFDP Number

907

CFDP Pages

27

Abstract

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.

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