We investigate the asymptotic behaviour of the median deviation and the semi-interquartile range based on the residuals from a linear regression model by deriving weak asymptotic representations for the estimators. These representations may be used to obtain a variety of central limit theorems and yield conditions under which the median deviation and the semi-interquartile range are asymptotically equivalent. The results justify the use of the estimators as concommitant scale estimators in the general scale equivariant M-estimation of a regression parameter problem. Finally, the results contain as a special case those obtained by Hall and Welsh (1985) for independent and identically distributed random variables.
Publié le : 1986-09-14
Classification:
Linear regression,
median deviation,
quantiles,
robust estimation,
scale estimation,
semi-interquartile range,
62F35,
60F05,
62G30
@article{1176350064,
author = {Welsh, A. H.},
title = {Bahadur Representations for Robust Scale Estimators Based on Regression Residuals},
journal = {Ann. Statist.},
volume = {14},
number = {2},
year = {1986},
pages = { 1246-1251},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350064}
}
Welsh, A. H. Bahadur Representations for Robust Scale Estimators Based on Regression Residuals. Ann. Statist., Tome 14 (1986) no. 2, pp. 1246-1251. http://gdmltest.u-ga.fr/item/1176350064/