CFDP 907

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


Publication Date: May 1989

Pages: 27


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.


Central limit theorem, empirical process, Fourier series, semiparametric estimator, time series

JEL Classification Codes:  211

See CFP: 792