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Independence Empirical Processes

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

Abstract

Let H be a probability measure on the measurable space (X x y, A x B) with marginal laws P and Q on (X, A) and (y, B), respectively. Given a sample (X 1, Y 1),..., (X n , Y n ) of independently and identically distributed vectors from H, we want to test the null hypothesis of independence H o : H = P x Q versus the alternative hypothesis H 1: HP x Q. Let H n be the empirical measure of the observations, and let P n , and Q n be its marginals. The latter are the empirical measures of the X i ’s and Yx’s, respectively.

Keywords

Null Hypothesis Covariance Function Gaussian Process Empirical Measure Original Observation 
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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