Monitoring random start forward searches for multivariate data

During a forward search from a robustly chosen starting point the plot of maximum Mahalanobis distances of observations in the subset may provide a test for outliers. This is not the customary test. We obtain distributional results for this distance during the search and exemplify its use. However, if clusters are present in the data, searches from random starts are required for their detection. We show that our new statistic has the same distributional properties whether the searches have random or robustly chosen starting points.