Pozivamo vas na 75. Fakultetski seminar 9. 10. 2025. u B3-37 u 12:15 na temu:
Antipodal Reflection Depth (ARD) with Application to Nonparametric Outlier Detection in Multivariate and Functional Data
koji će održati profesorica Regina Liu sa Sveučilište Rutgers iz Sjedinjenih Američkih Država.
Sažetak
Data depth, as a measure of centrality and center-outward ordering, has been developed into a powerful nonparametric alternative to the classical multivariate analysis or for functional data analysis. We introduce a general approach, referred to as antipodal reflection depth (ARD), to refine any existing notion of data depth (referred to as the base depth) to yield a class of new data depth. ARD has the desirable properties: i) It preserves the deepest point and the center-outward ordering along each ray from this deepest point obtained by the base depth; and ii) Its new center-outward ordering captures the relative magnitudes of deviation from all data points to the deepest point. The latter property is generally lacking in the existing notions of data depth due to their location-scale free nature. ARD combines the antipodal reflections of the original sample data in the calculation of depth values but draws inferences using only the original data with their associated ARD depth values. This approach is completely data driven and nonparametric. As an immediate application, ARD can be shown to be an effective approach for outlier detection in both multivariate and functional data. In addition to simulation studies, we also apply ARD to an analysis of aircraft landing performance to identify possible anomalous landings.
Kratki životopis
Regina Liu is Distinguished Professor, Rutgers University. Her research areas include data depth, resampling, nonparametric statistics, confidence distribution, and fusion learning. Aside from theoretical and methodological research, she has long collaborated with the FAA on aviation safety research projects on process control, text mining and risk management. She is an elected fellow of the Institute of Mathematical Statistics (IMS) and the American Statistical Association (ASA). She is the recipient of 2021 Noether Distinguished Scholar Award (ASA), 2024 Elizabeth Scott Award (Committee of Presidents of Statistical Societies (COPSS)), and the IMS 2025 Neyman Award & Lecture. She has served as Co-Editor for the Journal of the American Statistical Association and as Associate Editor for several journals. She was elected President of the Institute of Mathematical Statistics (IMS), 2020-2021.
