Insensitivity of Nadaraya–Watson estimators to design correlation

Yuliana Linke and Igor Borisov

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 19, 6909-6918

Abstract: 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.

Date: 2022
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DOI: 10.1080/03610926.2021.1876884

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