TY - JOUR
T1 - Insensitivity of Nadaraya–Watson estimators to design correlation
AU - Linke, Yuliana
AU - Borisov, Igor
N1 - Publisher Copyright:
© 2021 Taylor & Francis Group, LLC.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/2/1
Y1 - 2021/2/1
N2 - We show that Nadaraya–Watson estimators in nonparametric regression may be uniformly consistent without any specification of the design correlation structure. In contrast to the predecessors’ results, the design is not required to be fixed or consisted of independent or weakly dependent random variables under various dependence conditions, and the design random observations are not necessarily identically distributed and nondegenerate. We suggest a new simple sufficient condition on the design which provides the uniform consistency of such estimators. Key words and phrases: nonparametric regression, Nadaraya–Watson estimators, uniform consistency, strongly dependent data.
AB - We show that Nadaraya–Watson estimators in nonparametric regression may be uniformly consistent without any specification of the design correlation structure. In contrast to the predecessors’ results, the design is not required to be fixed or consisted of independent or weakly dependent random variables under various dependence conditions, and the design random observations are not necessarily identically distributed and nondegenerate. We suggest a new simple sufficient condition on the design which provides the uniform consistency of such estimators. Key words and phrases: nonparametric regression, Nadaraya–Watson estimators, uniform consistency, strongly dependent data.
KW - 62G08
UR - http://www.scopus.com/inward/record.url?scp=85100275617&partnerID=8YFLogxK
U2 - 10.1080/03610926.2021.1876884
DO - 10.1080/03610926.2021.1876884
M3 - Article
AN - SCOPUS:85100275617
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
SN - 0361-0926
ER -