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 $\beta$.
Publié le : 1982-06-14
Classification:
Feedback,
$M$-estimates,
non-constant variances,
random coefficient models,
weighted least squares,
62J05,
62G35
@article{1176345784,
author = {Carroll, Raymond J. and Ruppert, David},
title = {Robust Estimation in Heteroscedastic Linear Models},
journal = {Ann. Statist.},
volume = {10},
number = {1},
year = {1982},
pages = { 429-441},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345784}
}
Carroll, Raymond J.; Ruppert, David. Robust Estimation in Heteroscedastic Linear Models. Ann. Statist., Tome 10 (1982) no. 1, pp. 429-441. http://gdmltest.u-ga.fr/item/1176345784/