A2059
Title: Robust multiple change point detection for object data
Authors: Shojaeddin Chenouri - University of Waterloo (Canada) [presenting]
Abstract: A nonparametric multiple change point detection procedure is proposed for stochastic processes taking values on manifold-valued spaces $\mathcal{M}$. The proposed method is based on rank statistics constructed from intrinsic depth functions, allowing for the detection of changes in both location and scale without requiring parametric distributional assumptions. Finite-sample properties and asymptotic consistency results are established for the estimation of both the number and locations of change points. By expressing the test statistic as a U-statistic, sharp nonasymptotic bounds are derived for the proposed procedure. Robustness properties are investigated through breakdown value analysis and finite-sample Monte Carlo studies, demonstrating strong detection performance and stability under heavy-tailed distributions and contamination by outliers. The methodology is further illustrated through applications to real-world manifold-valued data arising in pedestrian surveillance video analysis, highway traffic monitoring, and vehicle health monitoring. Theoretical and empirical results confirm the effectiveness of the proposed nonparametric multiple change-point detection framework.
