Geodesic
Towards insensitivity of Nadaraya--Watson estimators with respect to design correlation
Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 2, pp. 236-252

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The consistency of Nadaraya–Watson estimators in nonparametric regression is proved without using traditional conditions for dependence of design elements (regressors). A design can be either fixed and not necessarily regular, or random and not necessarily satisfying classical correlation conditions for the design elements. A new characterization of the dependence of design elements is proposed, in terms of which sufficient conditions are formulated for both pointwise and uniform consistency of Nadaraya–Watson estimators.
Keywords: nonparametric regression, Nadaraya–Watson estimators, uniform consistency, fixed design, random design, strongly dependent design elements. 
@article{TVP_2023_68_2_a1,
     author = {Yu. Yu. Linke},
     title = {Towards insensitivity of {Nadaraya--Watson}  estimators with respect to design correlation},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {236--252},
     publisher = {mathdoc},
     volume = {68},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2023_68_2_a1/}
}
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Yu. Yu. Linke. Towards insensitivity of Nadaraya--Watson  estimators with respect to design correlation. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 2, pp. 236-252. http://geodesic.mathdoc.fr/item/TVP_2023_68_2_a1/