  In many applications, it is often of practical and scientific interest to
detect anomaly events in a streaming sequence of high-dimensional or
non-Euclidean observations. We study a non-parametric framework that utilizes
nearest neighbor information among the observations to detect changes in an
online setting. It can be applied to data in arbitrary dimension and
non-Euclidean data as long as a similarity measure on the sample space can be
defined. We consider new test statistics under this framework that can detect
anomaly events more effectively than the existing test while keeping the false
discovery rate controlled at a fixed level. Analytic formulas approximating the
average run lengths of the new approaches are derived to make them fast
applicable to modern datasets. Simulation studies are provided to support
theoretical results. The proposed approach is illustrated with an analysis of
the NYC taxi dataset.
