Rate of convergence of nonparametric estimates of maximum-likelihood type
type: Item
instance of: scholarly article
title: Rate of convergence of nonparametric estimates of maximum-likelihood type
zbMATH Open document ID: 0616.62048
author: Alexandre B. Tsybakov
author: Arkadi Nemirovski
author: Boris T. Polyak
published in: Problems of Information Transmission
publication date: 1985-01-01T00:00:00Z
review text: The authors obtain the rate of convergence for non-parametric regression M-estimators in \(L_ 2\). For a class of smooth, monotonic and convex functions, they show that this rate cannot be improved (to within a constant). A series of special cases is considered. The rate of convergence of the non-linear M-estimators is better than that of any linear estimator.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 3998995
zbMATH Keywords: upperbound for risk
zbMATH Keywords: maximum-likelihood type estimators
zbMATH Keywords: finite Fisher information
zbMATH Keywords: asymptotic form of minimax risk
zbMATH Keywords: rate of convergence
zbMATH Keywords: non- parametric regression M-estimators
zbMATH Keywords: non-linear M-estimators
zbMATH Keywords: linear estimator
reviewed by: A. K. Hosni
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3998995