Auxiliary results for "Nonparametric kernel estimation of the probability density function of regression errors using estimated residuals"

TL;DR

This supplemental document provides additional theoretical results supporting the main paper on nonparametric kernel estimation of regression error densities using residuals, enhancing the original study's rigor.

Contribution

It offers omitted theoretical details and proofs that strengthen the original nonparametric density estimation methodology for regression errors.

Findings

The supplemental material includes key theoretical lemmas and proofs.

It clarifies the asymptotic properties of the proposed estimators.

Supports the validity of the main paper's conclusions.

Abstract

This manuscript is a supplemental document providing the omitted material for our paper entitled "Nonparametric kernel estimation of the probability density function of regression errors using estimated residuals" [arXiv:1010.0439]. The paper is submitted to Journal of Nonparametric Statistics.