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Rates of Convergence

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

Abstract

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.

Keywords

Maximum Likelihood Estimator Regression Function Empirical Process Maximal Inequality Hellinger Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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