Professor Xiongtao Dai, UC Berkeley
Saturday April 29, 2023
4:20 pm - 4:45 pm
Tukey's Depth for Non-Euclidean Objects
Abstract
Data depth is a powerful nonparametric tool used to measure the centrality of an observation with respect to a distribution. We develop the metric halfspace depth, a data depth method applicable to objects lying on a general metric space, extending the well-known Tukey's depth for Euclidean data. The metric halfspace depth enjoys intuitive interpretation and leads to a center-outward ranking useful for data exploration. In addition, inferential methods such as robust location estimation and rank tests are also established. We will discuss the desirable statistical properties and efficient computation for the metric halfspace depth. The proposed method will be applied to reveal group differences in brain connectivity patterns among Alzheimer's disease patients.