Rates of Convergence

  • Aad W. van der Vaart
  • Jon A. Wellner
Part of the Springer Series in Statistics book series (SSS)


This chapter gives some results on rates of convergence of M-estimators, including maximum likelihood estimators and least-squares estimators. We first state an abstract result, which is a generalization of the theorem on rates of convergence in Chapter 3.2, and next discuss some methods to establish the maximal inequalities needed for the application of this result. Our main interest is in M-estimators of infinite-dimensional parameters.


Maximum Likelihood Estimator Regression Function Empirical Process Maximal Inequality Hellinger Distance 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Aad W. van der Vaart
    • 1
  • Jon A. Wellner
    • 2
  1. 1.Department of Mathematics and Computer ScienceFree UniversityAmsterdamThe Netherlands
  2. 2.StatisticsUniversity of WashingtonSeattleUSA

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