Uniform in bandwidth consistency of local polynomial regression function estimators

TL;DR

This paper extends a method for proving uniform in bandwidth consistency of kernel estimators, demonstrating its usefulness in establishing the consistency of local polynomial regression function estimators.

Contribution

It generalizes a previous proof technique to include local polynomial estimators, enhancing the theoretical understanding of their consistency properties.

Findings

Proves uniform in bandwidth consistency for local polynomial estimators.

Shows the method's applicability to regression function estimation.

Provides theoretical guarantees for local polynomial regression consistency.

Abstract

We generalize a method for proving uniform in bandwidth consistency results for kernel type estimators developed by the two last named authors. Such results are shown to be useful in establishing consistency of local polynomial estimators of the regression function.