Scan Statistics for Normal Data with Outliers

In this article we investigate the performance of scan statistics based on moving medians, as test statistics for detecting a local change in population mean, for one and two dimensional normal data, in presence of outliers, when the population variance is unknown. For fixed window scan statistics, both the training sample and parametric bootstrap methods are employed for one and two dimensional normal data, in presence of one or two outliers. Multiple window scan statistics are implemented via the parametric bootstrap method for one and two dimensional normal data, in presence of one or two outliers. Numerical results are presented via simulation to evaluate the power of these scan statistics for detecting the local change in the population mean, for selected parameters of the models characterizing the local change in the population mean and models characterizing the occurrence of one or two outliers in the data. When the window size where the local change of the population mean has occurred is unknown, the multiple window scan statistics, implemented via the bootstrap method, performed quite well.