A note on the rate of convergence of local polynomial estimators in regression models

Friedrich Liese; Ingo Steinke

Kybernetika (2001)

  • Volume: 37, Issue: 5, page [585]-603
  • ISSN: 0023-5954

Abstract

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Local polynomials are used to construct estimators for the value of the regression function and the values of the derivatives in a general class of nonparametric regression models. The covariables are allowed to be random or non-random. Only asymptotic conditions on the average distribution of the covariables are used as smoothness of the experimental design. This smoothness condition is discussed in detail. The optimal stochastic rate of convergence of the estimators is established. The results cover the special cases of regression models with i.i.d. errors and the case of observations at an equidistant lattice.

How to cite

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Liese, Friedrich, and Steinke, Ingo. "A note on the rate of convergence of local polynomial estimators in regression models." Kybernetika 37.5 (2001): [585]-603. <http://eudml.org/doc/33553>.

@article{Liese2001,
abstract = {Local polynomials are used to construct estimators for the value $m(x_\{0\})$ of the regression function $m$ and the values of the derivatives $D_\{\gamma \}m(x_\{0\})$ in a general class of nonparametric regression models. The covariables are allowed to be random or non-random. Only asymptotic conditions on the average distribution of the covariables are used as smoothness of the experimental design. This smoothness condition is discussed in detail. The optimal stochastic rate of convergence of the estimators is established. The results cover the special cases of regression models with i.i.d. errors and the case of observations at an equidistant lattice.},
author = {Liese, Friedrich, Steinke, Ingo},
journal = {Kybernetika},
keywords = {nonparametric regression models; smoothness condition; nonparametric regression models; smoothness condition},
language = {eng},
number = {5},
pages = {[585]-603},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A note on the rate of convergence of local polynomial estimators in regression models},
url = {http://eudml.org/doc/33553},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Liese, Friedrich
AU - Steinke, Ingo
TI - A note on the rate of convergence of local polynomial estimators in regression models
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 5
SP - [585]
EP - 603
AB - Local polynomials are used to construct estimators for the value $m(x_{0})$ of the regression function $m$ and the values of the derivatives $D_{\gamma }m(x_{0})$ in a general class of nonparametric regression models. The covariables are allowed to be random or non-random. Only asymptotic conditions on the average distribution of the covariables are used as smoothness of the experimental design. This smoothness condition is discussed in detail. The optimal stochastic rate of convergence of the estimators is established. The results cover the special cases of regression models with i.i.d. errors and the case of observations at an equidistant lattice.
LA - eng
KW - nonparametric regression models; smoothness condition; nonparametric regression models; smoothness condition
UR - http://eudml.org/doc/33553
ER -

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