A comparison between two robust regression estimators by means of robust covariances (Q1129815)

The stochastic linear regression model we consider is \(y_i= X_i^T\beta+ \varepsilon_i\), \(i=1,2,\dots, n\), where \((X_i,y_i)\), \(i=1,2,\dots, n\), is a sequence of i.i.d. random \(p\times 1\) vectors with a distribution \(F\). \(\varepsilon_i\) is independent of \(X_i\) for each \(i=1,2,\dots, n\), and the \(\varepsilon_i\)'s are i.i.d. errors with zero mean and variance \(\sigma^2\). Two classes of Mallows' GM-estimators with invariance are considered. Some of their asymptotic properties are described, and the fitted-value influence and variance components are compared by means of robust covariances.