Local Polynomial Variance-Function Estimation
(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:
https://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
- 0040-1706
- language
- English
- LU publication?
- yes
- id
- 59a2f996-fe54-4776-9dcc-b9e134883ad0 (old id 1214783)
- date added to LUP
- 2016-04-01 16:31:26
- date last changed
- 2022-03-15 01:06:57
@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}},
keywords = {{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}},
}