Advanced

Local Polynomial Variance-Function Estimation

Ruppert, David; Wand, Matt, P.; Holst, Ulla LU and Hössjer, Ola LU (1997) In Technometrics 39(3). p.262-273
Abstract
The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focused on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The biasing effect of preliminary estimation of the mean is studied, and a degrees-of-freedom correction of bias is proposed. The corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known. A proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions. The proposal is... (More)
The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focused on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The biasing effect of preliminary estimation of the mean is studied, and a degrees-of-freedom correction of bias is proposed. The corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known. A proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions. The proposal is illustrated with data from the LIDAR method of measuring atmospheric pollutants and from turbulence-model computations. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
smoother matrix, regression, nonparametric, kernel smoothing, Bandwidth, heteroscedasticity
in
Technometrics
volume
39
issue
3
pages
262 - 273
publisher
American Statistical Association
external identifiers
  • scopus:0031199387
ISSN
0040-1706
language
English
LU publication?
yes
id
59a2f996-fe54-4776-9dcc-b9e134883ad0 (old id 1214783)
date added to LUP
2008-08-14 13:39:08
date last changed
2017-08-06 04:35:00
@article{59a2f996-fe54-4776-9dcc-b9e134883ad0,
  abstract     = {The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focused on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The biasing effect of preliminary estimation of the mean is studied, and a degrees-of-freedom correction of bias is proposed. The corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known. A proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions. The proposal is illustrated with data from the LIDAR method of measuring atmospheric pollutants and from turbulence-model computations.},
  author       = {Ruppert, David and Wand, Matt, P. and Holst, Ulla and Hössjer, Ola},
  issn         = {0040-1706},
  keyword      = {smoother matrix,regression,nonparametric,kernel smoothing,Bandwidth,heteroscedasticity},
  language     = {eng},
  number       = {3},
  pages        = {262--273},
  publisher    = {American Statistical Association},
  series       = {Technometrics},
  title        = {Local Polynomial Variance-Function Estimation},
  volume       = {39},
  year         = {1997},
}