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Bahadur-Kiefer Approximation for Spatial Quantiles

  • V. Koltchinskii
Conference paper
Part of the Progress in Probability book series (PRPR, volume 35)

Abstract

Let F be the uniform distribution on [0,1], (X 1, …,X n) be a sample from the distribution F, and F n be the empirical distribution based on this sample. Let F -1 be the quantile function of F (which, of course, coincides with F in the case of uniform distribution F) and let F n -1 be the empirical quantile function. Let us define r n(t):= F n -1(t)- F n-1(t) + F n(t)- F(t),t ∈ [0,1]. Bahadur (1966) and Kiefer (1967), 1970) (see also Shorack and Wellner (1986) for further references) investigated the asymptotic behavior of the process r n. It appeared that for any t ∈ (0,1) n 3/4 r n(t) converges weakly to a certain limit distribution.

Keywords

Unit Ball Oscillation Behavior Empirical Process Iterate Logarithm Quantile Function 
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 1994

Authors and Affiliations

  • V. Koltchinskii
    • 1
  1. 1.Mathematisches InstitutJustus-Liebig UniversitätGiessenGermany

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