Central Limit and Functional Central Limit Theorems for Hilbert-Valued Dependent Heterogeneous Arrays with Applications

UCSD Economics Discussion Paper 92-35R

35 Pages Posted: 6 Jan 1998

See all articles by Xiaohong Chen

Xiaohong Chen

Yale University - Cowles Foundation

Halbert L. White, Jr.

University of California, San Diego (UCSD) - Department of Economics

Date Written: June 1997

Abstract

We obtain new CLTs and FCLTs for Hilbert-valued arrays near epoch dependent on mixing processes, as well as new FCLTs for general Hilbert-valued adapted dependent heterogeneous arrays. These theorems are useful in delivering asymptotic distributions for parametric and nonparametric estimators and their functionals in time series econometrics. We give three significant applications for near epoch dependent observations: (1) A new CLT for any plug-in estimator of a cumulative distribution function (e.g., an empirical cdf, or a cdf estimator based on a kernel density estimator), which can in turn deliver distribution results for many Von Mises functionals; (2) A new limiting distribution result for degenerate U-statistics, which delivers distribution results for Bierens' integrated conditional moment tests; (3) A new functional central limit result for Hilbert-valued stochastic approximation procedures, which delivers distribution results for nonparametric recursive generalized method of moment estimators, including nonparametric adaptive learning models.

JEL Classification: C12, C13

Suggested Citation

Chen, Xiaohong and White, Halbert L., Central Limit and Functional Central Limit Theorems for Hilbert-Valued Dependent Heterogeneous Arrays with Applications (June 1997). UCSD Economics Discussion Paper 92-35R, Available at SSRN: https://ssrn.com/abstract=51140 or http://dx.doi.org/10.2139/ssrn.51140

Xiaohong Chen

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Halbert L. White (Contact Author)

University of California, San Diego (UCSD) - Department of Economics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States
858-534-3502 (Phone)
858-534-7040 (Fax)

HOME PAGE: http://www.econ.ucsd.edu/~mbacci/white/