## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 25, Number 2 (1954), 218-251.

### Asymptotic Distribution of Serial Statistics and Applications to Problems of Nonparametric Tests of Hypotheses

#### Abstract

The asymptotic distribution of a class of statistics, which has been called serial statistics, has been obtained, for permutations of the observed sample values. Specific instances of the use of such statistics, for the test of randomness of a sequence, have been given and the large sample power functions have been considered, when the alternative is a Markov process.

#### Article information

**Source**

Ann. Math. Statist., Volume 25, Number 2 (1954), 218-251.

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177728783

**Digital Object Identifier**

doi:10.1214/aoms/1177728783

**Mathematical Reviews number (MathSciNet)**

MR61323

**Zentralblatt MATH identifier**

0056.13301

**JSTOR**

links.jstor.org

#### Citation

Ghosh, M. N. Asymptotic Distribution of Serial Statistics and Applications to Problems of Nonparametric Tests of Hypotheses. Ann. Math. Statist. 25 (1954), no. 2, 218--251. doi:10.1214/aoms/1177728783. https://projecteuclid.org/euclid.aoms/1177728783