The Annals of Mathematical Statistics

Distribution Free Tests of Independence Based on the Sample Distribution Function

J. R. Blum, J. Kiefer, and M. Rosenblatt

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Abstract

Certain tests of independence based on the sample distribution function (d.f.) possess power properties superior to those of other tests of independence previously discussed in the literature. The characteristic functions of the limiting d.f.'s of a class of such test criteria are obtained, and the corresponding d.f. is tabled in the bivariate case, where the test is equivalent to one originally proposed by Hoeffding [4]. A discussion is included of the computational problems which arise in the inversion of characteristic functions of this type. Techniques for computing the statistics and for approximating the tail probabilities are considered.

Article information

Source
Ann. Math. Statist. Volume 32, Number 2 (1961), 485-498.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoms/1177705055

Digital Object Identifier
doi:10.1214/aoms/1177705055

Mathematical Reviews number (MathSciNet)
MR125690

JSTOR
links.jstor.org

Citation

Blum, J. R.; Kiefer, J.; Rosenblatt, M. Distribution Free Tests of Independence Based on the Sample Distribution Function. Ann. Math. Statist. 32 (1961), no. 2, 485--498. doi:10.1214/aoms/1177705055. http://projecteuclid.org/euclid.aoms/1177705055.


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