Estimation of Heteroscedasticity in Regression Analysis

1987/06/01 by Hans‐Georg Müller, Ulrich Stadtmüller · 4 citations
Mathematics · #Statistical Methods and Inference #Advanced Statistical Methods and Models #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.1214/aos/1176350364

openalex publication_date 1987/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

Consider the regression model Y_i = g(t_i) + ε_i, 1 ≤ i ≤ n, with nonrandom design variables (t_i) and measurements (Y_i) for the unknown regression function g(⋅). We assume that the data are heteroscedastic, i.e., E(ε²_i) = σ²_i \not≡ const. and investigate how to estimate σ²_i. If σ²_i = σ²(t_i) with a smooth function σ²(⋅), initial estimators σ²_i can be improved by kernel smoothers and the resulting class of estimators is shown to be uniformly consistent. These estimates can be used to improve the estimation of the regression function g itself in parametric and nonparametric models. Further applications are suggested.

Citations

• Remarks on Some Nonparametric Estimates of a Density Function
• Adapting for Heteroscedasticity in Linear Models

Cited by

• On a Semiparametric Variance Function Model and a Test for Heteroscedasticity
• Functional Variance Processes
• Nonparametric estimation in a regression model with additive and multiplicative noise
• Variance function [wikipedia]