Moment convergence of M-estimators



This study extends the rate of convergence theorem of M-estimators presented by van der Vaart and Wellner (weak convergence and empirical processes: with applications to statistics, Springer-Verlag, Newyork, 1996) who gave a result of the form r inline image to a result of the form supnE | r inline image, for any p≥1. This result is useful for deriving the moment convergence of the rescaled residual. An application to maximum likelihood estimators is discussed.