Hoeffding’s Independence Test

  • N. I. Fisher
  • P. K. Sen
Chapter
Part of the Springer Series in Statistics book series (SSS)

Abstract

Let the random vector (X, Y) have the cumulative distribution function * (CDF) F(x, y). Let ℱ be the class of all continuous bivariate CDFs, and ℱ0 be the class of all F ∈ ℱ such that F(x, y) = F(x, ∞) F(∞, y), Assume that F ∈ ℱ. The hypothesis H 0 that X and Y are independent is equivalent to the hypothesis that F ∈ ℱ0.

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References

  1. [1]
    Blum, J. R., Kiefer, J., and Rosenblatt, M. (1961). Ann. Math. Statist., 32, 485–498.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Csörgö, M. (1979). J. Multivariate Anal., 9,84–100.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Hoeffding, W. (1948). Ann. Math. Statist., 19, 546–557.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • N. I. Fisher
    • 1
  • P. K. Sen
    • 2
  1. 1.Division of Mathematics and StatisicsCSIRONorth RydeAustralia
  2. 2.Department of StatisticsUniversity of North Carolina at Chapel HillChapel HillUSA

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