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June, 1961 Distribution Free Tests of Independence Based on the Sample Distribution Function
J. R. Blum, J. Kiefer, M. Rosenblatt
Ann. Math. Statist. 32(2): 485-498 (June, 1961). DOI: 10.1214/aoms/1177705055


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.


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J. R. Blum. J. Kiefer. M. Rosenblatt. "Distribution Free Tests of Independence Based on the Sample Distribution Function." Ann. Math. Statist. 32 (2) 485 - 498, June, 1961.


Published: June, 1961
First available in Project Euclid: 27 April 2007

zbMATH: 0139.36301
MathSciNet: MR125690
Digital Object Identifier: 10.1214/aoms/1177705055

Rights: Copyright © 1961 Institute of Mathematical Statistics

Vol.32 • No. 2 • June, 1961
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