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 . The asymptotic distribution of 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.
Citation
Noel Cressie. "The Asymptotic Distribution of the Scan Statistic Under Uniformity." Ann. Probab. 8 (4) 828 - 840, August, 1980. https://doi.org/10.1214/aop/1176994669
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