Estimating Tukey Depth Using Incremental Quantile Estimators

Abstract

The concept of depth represents methods to measure how deep an arbitrary point is positioned in a dataset and can be seen as the opposite of outlyingness. It has proved very useful and a wide range of methods have been developed based on the concept. To address the well-known computational challenges associated with the depth concept, we suggest to estimate Tukey depth contours using recently developed incremental quantile estimators. The suggested algorithm can estimate depth contours when the dataset in known in advance, but also recursively update and even track Tukey depth contours for dynamically varying data stream distributions. Tracking was demonstrated in a real-life data example where changes in human activity was detected in real-time from accelerometer observations.