Publication at Faculty of Mathematics and Physics |
2010
Abstract
In this paper we find verifiable regularity conditions to ensure that S-estimators of scale and regression and MM-estimators of regression are uniformly consistent and uniformly asymptotically normally distributed over contamination neighbourhoods. Moreover, we show how to calculate the size of these neighbour- hoods.
In particular, we find that, for MM-estimators computed with Tukey’s family of bisquare score functions, there is a trade-off between the size of these neighbourhoods and both the breakdown point of the S-estimators and the leverage of the contamination that is allowed in the neighbourhood. These results extend previous work of Salibian-Barrera and Zamar for location-scale to the linear regression model.