Fast and stable bootstrap methods for robustestimates

摘要

The standard error and sampling distribution of robust estimates can, in principle,rnbe estimated using the bootstrap. However, two problems arise when wernwant to use bootstrap with robust estimates on moderately large data sets: thernbootstrap estimates may be unrealiable because the proportion of outliers in manyrnbootstrap samples could be higher than that in the original data set, and the highrncomputational demand of robust regression estimates may render the method unfeasiblernfor moderately high-dimensional problems. Recently, Salibian-Barrera andrnZamar (2002) have proposed a new bootstrap method called robust bootstrap to estimaternthe asymptotic distribution and asymptotic variance of MM-estimates. Thisrnmethod overcomes the problems mentioned above, namely: it is fast and stable (itrncan resist large proportion of outliers on the bootstrap samples). Unfortunately,rnits convergence seems to be only of order Op(1/(√n)). Another way to estimate thernasymptotic variance of robust estimates on large datasets is to bootstrap a onesteprnNewton-Raphson iteration of their estimating equations. This method willrntypically be fast (and hence feasible on moderately large datasets). In this paperrnwe compare the performance of this method with that of the robust bootstrap forrnthe simple location-scale model.