Open Access
June, 1982 Robust Estimation in Heteroscedastic Linear Models
Raymond J. Carroll, David Ruppert
Ann. Statist. 10(2): 429-441 (June, 1982). DOI: 10.1214/aos/1176345784


We consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter $\theta$. We propose robust estimates for the regression parameter $\beta$ and show that, as long as a reasonable starting estimate of $\theta$ is available, our estimates of $\beta$ are asymptotically equivalent to the natural estimate obtained with known variances. A particular method for estimating $\theta$ is proposed and shown by Monte-Carlo to work quite well, especially in power and exponential models for the variances. We also briefly discuss a "feedback" estimate of $\beta$.


Download Citation

Raymond J. Carroll. David Ruppert. "Robust Estimation in Heteroscedastic Linear Models." Ann. Statist. 10 (2) 429 - 441, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0497.62034
MathSciNet: MR653518
Digital Object Identifier: 10.1214/aos/1176345784

Primary: 62J05
Secondary: 62G35

Keywords: $M$-estimates , Feedback , non-constant variances , random coefficient models , weighted least squares

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
Back to Top