We discuss the asymptotic linearization of multivariate M-estimators, when the limit distribution is stable. We consider two different types of kernels: VC and bracketing. When applied to the case of normal limits, our work improves the known results to obtain the limit distribution of...

A large deviation principle for U-statistics is presented. It relies on the large deviation for B-valued r.v. and on the spectral decomposition of the kernel of the U-statistic.