## The Annals of Mathematical Statistics

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

### Distribution Free Tests of Independence Based on the Sample Distribution Function

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

#### 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**

https://projecteuclid.org/euclid.aoms/1177705055

**Digital Object Identifier**

doi:10.1214/aoms/1177705055

**Mathematical Reviews number (MathSciNet)**

MR125690

**Zentralblatt MATH identifier**

0139.36301

**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. https://projecteuclid.org/euclid.aoms/1177705055.