A new adaptive procedure for multiple window scan statistics

Scan statistics have been widely applied to test for unusual cluster of events in many scientific areas. It has been of practical interest on how to select the window size of a scan statistic. An adaptive procedure for multiple window scan statistics is proposed and the distributions are studied for independent identically distributed Bernoulli trials and uniform observations on (0, 1) in one-dimensional case. The idea of the procedure is to select the window sizes sequentially. An initial window size is chosen and the subsequent window sizes are then determined, depending on the value of the current scan statistic at each stage. The power of scan statistics based on the adaptive procedure is compared with power of standard scan statistics. Numerical results and applications for disease clusters detection are given to illustrate our procedure.