Insensitivity of Nadaraya–Watson estimators to design correlation

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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.

Original languageEnglish
JournalCommunications in Statistics - Theory and Methods
Early online date1 Feb 2021
Publication statusE-pub ahead of print - 1 Feb 2021


  • 62G08


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