## The Annals of Statistics

### Robust Estimation in Heteroscedastic Linear Models

#### Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176345784

Digital Object Identifier
doi:10.1214/aos/1176345784

Mathematical Reviews number (MathSciNet)
MR653518

JSTOR