On Sufficient Conditions for the Consistency of Local Linear Kernel Estimators

Yu. Yu. Linke

Matematičeskie zametki, Tome 114 (2023) no. 3, pp. 353-369.

Résumé

The consistency of classical local linear kernel estimators in nonparametric regression is proved under constraints on design elements (regressors) weaker than those known earlier. The obtained conditions are universal with respect to the stochastic nature of design, which may be both fixed regular and random and is not required to consist of independent or weakly dependent random variables. Sufficient conditions for pointwise and uniform consistency of classical local linear estimators are stated in terms of the asymptotic behavior of the number of design elements in certain neighborhoods of points in the domain of the regression function.

Détail

Keywords: nonparametric regression, local linear estimator, uniform consistency, fixed design, random design, highly dependent design elements.

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