Local Polynomial VarianceFunction Estimation
(1997) In Technometrics 39(3). p.262273 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 degreesoffreedom 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 degreesoffreedom 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 turbulencemodel computations. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1214783
 author
 Ruppert, David; Wand, Matt, P.; Holst, Ulla ^{LU} and Hössjer, Ola ^{LU}
 organization
 publishing date
 1997
 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
 00401706
 language
 English
 LU publication?
 yes
 id
 59a2f996fe5447769dccb9e134883ad0 (old id 1214783)
 date added to LUP
 20080814 13:39:08
 date last changed
 20181121 20:42:04
@article{59a2f996fe5447769dccb9e134883ad0, 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 degreesoffreedom 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 turbulencemodel computations.}, author = {Ruppert, David and Wand, Matt, P. and Holst, Ulla and Hössjer, Ola}, issn = {00401706}, keyword = {smoother matrix,regression,nonparametric,kernel smoothing,Bandwidth,heteroscedasticity}, language = {eng}, number = {3}, pages = {262273}, publisher = {American Statistical Association}, series = {Technometrics}, title = {Local Polynomial VarianceFunction Estimation}, volume = {39}, year = {1997}, }