## The Annals of Probability

### The Asymptotic Distribution of the Scan Statistic Under Uniformity

Noel Cressie

#### Abstract

The problem of testing uniformity on [0, 1] against a clustering alternative, is considered. Naus has shown that the generalized likelihood ratio test yields the scan statistic $N(d)$. The asymptotic distribution of $N(d)$ under the null hypothesis of uniformity is considered herein, and related to the version of the scan statistic defined for points from a Poisson process. An application of the above yields distributional results for the supremum of a stationary Gaussian process with a correlation function that is tent-like in shape, until it flattens out at a constant negative value.

#### Article information

Source
Ann. Probab., Volume 8, Number 4 (1980), 828-840.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994669

Digital Object Identifier
doi:10.1214/aop/1176994669

Mathematical Reviews number (MathSciNet)
MR577319

Zentralblatt MATH identifier
0438.60035

JSTOR
links.jstor.org

#### Citation

Cressie, Noel. The Asymptotic Distribution of the Scan Statistic Under Uniformity. Ann. Probab. 8 (1980), no. 4, 828--840. doi:10.1214/aop/1176994669. https://projecteuclid.org/euclid.aop/1176994669