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Keywords:

  • M-estimator;
  • rate of convergence;
  • moment convergence

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.