Change-Detection-Assisted Multiple Testing for Spatiotemporal Data

• Activity Number: 412 - Theory and Methods for Change-Point and Abnormality Detection
• Type: Contributed
• Date/Time: Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Lilun Du* and Yunlong Wang and Changliang Zou and Zhaojun Wang
• Companies: HKUST and Nankai University and Nankai University and Nankai University
• Keywords: Spatiotemporal dependence; False discovery rate; Feature screening; High-dimensionality; Kernel smoothing; Multiple change points model

Abstract

We consider large-scale multiple testing of data with spatially and temporally clustered signals. When the conventional false discovery rate (FDR) procedure is applied without taking into account the clustering structure, the power to detect statistical significance tends to be reduced. We formulate a spatiotemporal framework in the presence of multiple change points for multiple testing, and propose a data-driven procedure that aims to fully utilize the clustering information. With the aim of grouping data into several sets, we develop a new change-point detection algorithm that integrates the kernel-based aggregation of spatial observations with a global loss function at the temporal level. Then, we derive an FDR control scheme for set-wise multiple testing. Under some mild conditions on the spatiotemporal dependence structure, the FDR is shown to be strongly controlled. Theoretical analysis and numerical studies demonstrate the advantages of our algorithm over competing methods.