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.

PY - 2022

Y1 - 2022

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

VL - 51

SP - 6909

EP - 6918

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 19

ER -