On the estimation of the derivatives of a function with the derivatives of an estimate
type: Item
instance of: scholarly article
title: On the estimation of the derivatives of a function with the derivatives of an estimate
zbMATH Open document ID: 0665.62041
DOI: 10.1016/0047-259X(89)90102-4
author: Yannis G. Yatracos
published in: Journal of Multivariate Analysis
publication date: 1989-01-01T00:00:00Z
review text: Let \({\tilde \theta}{}_ n(x)\) be an estimator of a smooth function \(\theta\) (x). It is proved that \(\theta\) (x) can be estimated easier than its derivative \(\theta^{(s)}(x)\), providing for \(\| {\hat \theta}_ n^{(s)}-\theta^{(s)}\|_ q\) an upper bound that depends on \(\| {\hat \theta}_ n-\theta \|_ q\). The same bound can be used as a tool to derive automatically rates of convergence when we are estimating derivatives of densities or regression functions.
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 4088733
zbMATH Keywords: bounds on norm differences of derivatives of smooth functions
zbMATH Keywords: rates of convergence
zbMATH Keywords: estimating derivatives of densities
MaRDI profile type: Publication
cites work: Q5555375
cites work: Q4064526
cites work: Q3845688
cites work: Q3719633
description: scientific article; zbMATH DE number 4088733