This week's Graduate Student Seminar speaker is Nicholas James, from ORIE.
Talk Title: A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data
Abstract
Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. For a set of multivariate observations of arbitrary dimension, we consider nonparametric estimation of both the number of change points and the positions at which they occur. We do not make any assumptions regarding the nature of the change in distribution or any distribution assumptions beyond the existence of the αth absolute moment, for some α ∈ (0, 2). Estimation is based on hierarchical clustering and we propose both divisive and agglomerative algorithms. The divisive method is shown to provide consistent estimates of both the number and location of change points under standard regularity assumptions. We compare the proposed approach with competing methods in a simulation study. Methods from cluster analysis are applied to assess performance and to allow simple comparisons of location estimates, even when the estimated number differs.