Asymptotically efficient estimators for nonparametric heteroscedastic regression models

2007/11/29 by Jean-Yves Brua, Brua, Jean-Yves
Engineering · Mathematics · #62G08 #62G20 #Advanced Statistical Methods and Models #Control Systems and Identification #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62G08 #msc:62G20 #stat.TH

paper · pdf · doi:10.48550/arxiv.0711.4725

arxiv created 2007/11/29 · openalex publication_date 2007/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel estimator is constructed for the minimax absolute error risk.

Related

• Adaptive nonparametric estimation in heteroscedastic regression models. Part 2: Asymptotic efficiency
• Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression via model selection
• Adaptive nonparametric estimation in heteroscedastic regression models. Part 1: Sharp non-asymptotic Oracle inequalities
• Nonparametric estimation for an autoregressive model
• Nonparametric estimation in a semimartingale regression model. Part 2. Robust asymptotic efficiency