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Central limit theorems for nonparametric estimators with real‐time random variables
Author(s) -
Kim Tae Yoon,
Luo ZhiMing
Publication year - 2010
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2010.00668.x
Subject(s) - estimator , nonparametric statistics , mathematics , nonparametric regression , central limit theorem , limit (mathematics) , discretization , random variable , sequence (biology) , statistics , mathematical analysis , biology , genetics
In this article, asymptotic theories for nonparametric methods are studied when they are applied to real‐time data. In particular, we derive central limit theorems for nonparametric density and regression estimators. For this we formally introduce a sequence of real‐time random variables indexed by a parameter related to fine gridding of time domain (or fine discretization). Our results show that the impact of fine gridding is greater in the density estimation case in the sense that strong dependence due to fine gridding severely affects the major strength of nonparametric density estimator (or its data‐adaptive property). In addition, we discuss some issues about nonparametric regression model with fine gridding of time domain.