Wilcoxon Rank Sum Scan Statistics for Continuous Data with Outliers

In this chapter, we investigate the performance of several Wilcoxon rank sum scan statistics in detecting a local change in population mean, in the presence of outliers, for one- and two-dimensional data, generated by a continuous distribution. The detection problem is formulated via testing of hypotheses and implemented via simulation using a nonparametric bootstrap approach. The performance of the Wilcoxon rank sum scan statistics discussed in this chapter is evaluated via simulation based on the accuracy of achieving the specified significance level and the power against selected alternatives. The selected alternative hypotheses are based on probability models for the observed data, probability models for the outliers, and their location in the data and selected parameters indicating the local change in the population mean. Directions for future research are discussed as well in this chapter.