Maximum scan score-type statistics

In this article we introduce a maximum scan score-type statistic for testing the null hypothesis that the observations are iid according to a specified distribution, against an alternative that the observations cluster within a window of unknown length. This statistic is a variable window scan statistic, based on a finite number of standardized fixed window scan statistics. Approximations for the significance level of this statistic are derived for 0-1 iid Bernoulli trials and for iid uniform observations on the interval [0,1). The advantage in using a maximum scan score-type statistic, rather than a single fixed window scan statistic, is that it is more effective in detecting window-type clustering of observations.