Central limit theorem for nonparametric regression under dependent data

Abstract

This paper is concerned with estimating nonparametric regression function g on the basis of noisy observations taken at nonrandom design points xni. Such noises ξi’s are linear combinations of weakly dependent random variables satisfying certain assumptions and weighted sum of negatively associated random variables respectively. The main result of this study is that, the normalized version of a general linear smoother of the form gn(x) = ∑in=1 ωni(x)Yni are asymptotically normal for these two cases.

Date of Award	2003
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology