Two multivariate online change detection models.

Online change point detection methods monitor changes in the distribution of a data stream. This article discusses two non-parametric online change detection methods based on the energy statistics and Mahalanobis depth. To apply the energy statistic, we use sliding-window algorithm with efficient training and updating procedures. For Mahalanobis depth, we propose an algorithm to train the threshold with desired protective ability against false alarms and discuss factors that have an influence on the threshold. Numerical studies evaluate and compare the performance of the proposed models with three existing methods to detect changes in the mean and variability of a data stream. The methods are applied to detecting changes in the flowing volume of the Mississippi River.

Depth functions and mutidimensional medians on minimal spanning trees.

Based on the minimal spanning tree (MST) of the observed data set, the paper introduces new notions of data depth and medians for multivariate data. The MST of a data set of size n is the MST of the complete weighted undirected graph on n vertices, where the edge weights are the pairwise distances of the data points. We study several properties of the MST-based depth functions. We consider the corresponding multidimensional medians, investigate their robustness and computational complexity. An example illustrates the use of the MST-based depth functions.