The Annals of Statistics

Adapting for Heteroscedasticity in Linear Models

Raymond J. Carroll

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Abstract

In a heteroscedastic linear model, it is known that if the variances are a parametric function of the design, then one can construct an estimate of the regression parameter which is asymptotically equivalent to the weighted least squares estimate with known variances. We show that the same is true when the only thing known about the variances is that they are determined by an unknown but smooth function of the design or the mean response.

Article information

Source
Ann. Statist. Volume 10, Number 4 (1982), 1224-1233.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176345987

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176345987

Mathematical Reviews number (MathSciNet)
MR673657

Zentralblatt MATH identifier
0571.62058

Subjects
Primary: 62J05: Linear regression
Secondary: 62G35: Robustness

Keywords
Linear models regression heteroscedasticity nonparametric nonparametric regression

Citation

Carroll, Raymond J. Adapting for Heteroscedasticity in Linear Models. The Annals of Statistics 10 (1982), no. 4, 1224--1233. doi:10.1214/aos/1176345987. http://projecteuclid.org/euclid.aos/1176345987.


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