Journal of Mathematical Sciences

, Volume 89, Issue 5, pp 1486–1494 | Cite as

A consistent modification of a test for independence based on the empirical characteristic function

  • A. Kankainen
  • N. G. Ushakov


A modification of a test for independence based on the empirical characteristic function is investigated. The initial test is not consistent in the general case. The modification makes the test always consistent and asymptotically distribution free. It is based on a special transformation of the data.


Characteristic Function Initial Test Special Transformation Consistent Modification Empirical Characteristic 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. R. Blum, J. Kiefer, and M. Rosenblatt, “Distribution free tests of independence based on the sample distribution function,”Ann. Math. Statist.,32, 485–498 (1961).MathSciNetGoogle Scholar
  2. 2.
    S. Csörgő, “Limit behavior of the empirical characteristic function,”Ann. Probab.,9, No. 1, 130–144 (1981).MathSciNetGoogle Scholar
  3. 3.
    S. Csörgő, “Multivariate empirical characteristic functions,”Z. Wahrscheinlichkeitstheorie verw. Gebiete.,55, 203–229 (1981).Google Scholar
  4. 4.
    S. Csörgő, “Testing for independence by the empirical characteristic function,”J. Multivariate Anal.,16, 290–299 (1985).MathSciNetGoogle Scholar
  5. 5.
    R. Cuppens,Decomposition of Multivariate Characteristic Functions, Academic Press, New York (1975).Google Scholar
  6. 6.
    D. Dugué, “Sur des tests d'indépendance ‘indépendants de la loi’,”C. R. Acad. Sci. Paris Série A,281, 1103–1104 (1975).MATHGoogle Scholar
  7. 7.
    A. Feuerverger, “A consistent test for bivariate dependence,”Int. Statist. Rev. 61, 419–433 (1993).MATHGoogle Scholar
  8. 8.
    W. Hoeffding, “A nonparametric test for independence,”Ann. Math. Statist.,19, 546–557 (1948).MATHMathSciNetGoogle Scholar
  9. 9.
    A. Kankainen,Consistent Testing of Total Independence Based on the Empirical Characteristic Function, Ph. D. Thesis, Jyväskylä Univ. Press, Jyväskylä (1995).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • A. Kankainen
    • 1
  • N. G. Ushakov
    • 2
  1. 1.University of JyväskyläJyväskyläFinland
  2. 2.Institute of Microelectronics TechnologyRussian Academy of SciencesChernogolovkaRussia

Personalised recommendations