Rates of strong uniform consistency for the $k$-nearest neighbors kernel estimators of density and regression function

TL;DR

This paper establishes the rates of strong uniform consistency for $k$-nearest neighbors kernel estimators of density and regression functions in multivariate settings, providing theoretical guarantees across the entire space.

Contribution

It introduces new rates of strong uniform consistency for $k$-nearest neighbors kernel estimators in multivariate cases, under specific assumptions.

Findings

Derived explicit rates of strong uniform consistency

Applicable to multivariate density and regression estimation

Provides theoretical guarantees over the entire space

Abstract

We adress the problem of consistency of the $k$-nearest neighbors kernel estimators of the density and the regression function in the multivariate case. We get the rates of strong uniform consistency on the whole space $\mathbb{R}^p$ for these estimators under specified assumptions.