The Annals of Statistics

Robust Estimation in Heteroscedastic Linear Models

Raymond J. Carroll and David Ruppert

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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 $\beta$.

Article information

Ann. Statist. Volume 10, Number 2 (1982), 429-441.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)


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

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


Carroll, Raymond J.; Ruppert, David. Robust Estimation in Heteroscedastic Linear Models. Ann. Statist. 10 (1982), no. 2, 429--441. doi:10.1214/aos/1176345784.

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