Efficient estimation of the error distribution function in heteroskedastic nonparametric regression with missing data

TL;DR

This paper introduces a residual-based empirical distribution function to accurately estimate the error distribution in heteroskedastic nonparametric regression models with missing data, demonstrating asymptotic optimality.

Contribution

It proposes a new estimator for the error distribution function that is asymptotically most precise in the context of heteroskedastic nonparametric regression with missing responses.

Findings

Estimator is asymptotically most precise

Effective with responses missing at random

Applicable to heteroskedastic nonparametric models

Abstract

A residual-based empirical distribution function is proposed to estimate the distribution function of the errors of a heteroskedastic nonparametric regression with responses missing at random based on completely observed data, and this estimator is shown to be asymptotically most precise.