Distribution Free Tests of Independence Based on the Sample Distribution Function

  • Blum J
  • Kiefer J
  • Rosenblatt M
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Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Institute of Mathematical Statistics is collaborating with JSTOR to digitize, preserve and extend access to The Annals of Mathematical Statistics. 0. Summary. 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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Blum, J. R., Kiefer, J., & Rosenblatt, M. (1961). Distribution Free Tests of Independence Based on the Sample Distribution Function. The Annals of Mathematical Statistics, 32(2), 485–498. https://doi.org/10.1214/aoms/1177705055

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