## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 27, Number 2 (1956), 540-543.

### A Vector Form of the Wald-Wolfowitz-Hoeffding Theorem

#### Abstract

Hotelling and Pabst [1] showed that the rank correlation coefficient had a limiting normal distribution under the equally likely permutations of the hypothesis of independence. Wald and Wolfowitz [2] developed a general theorem of this type, and Noether [3] and Hoeffding [4] have relaxed the conditions used therein. In this paper a vector form of the theorem is proved along the lines used in an example by Wald and Wolfowitz [1] but taking account of the singular cases in which the correlations approach one.

#### Article information

**Source**

Ann. Math. Statist., Volume 27, Number 2 (1956), 540-543.

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177728279

**Digital Object Identifier**

doi:10.1214/aoms/1177728279

**Mathematical Reviews number (MathSciNet)**

MR78597

**Zentralblatt MATH identifier**

0070.36402

**JSTOR**

links.jstor.org

#### Citation

Fraser, D. A. S. A Vector Form of the Wald-Wolfowitz-Hoeffding Theorem. Ann. Math. Statist. 27 (1956), no. 2, 540--543. doi:10.1214/aoms/1177728279. https://projecteuclid.org/euclid.aoms/1177728279