A0331
Title: Statistical inference for non-Euclidean valued time series
Authors: Xiaofeng Shao - University of Illinois at Urbana-Champaign (United States) [presenting]
Feiyu Jiang - Fudan University (China)
Changbo Zhu - University of Notre Dame (United States)
Abstract: Data objects taking value in a general metric space have become increasingly common in modern data analysis. The focus is on two important statistical inference problems, namely, two-sample testing and change-point detection, for such non-Euclidean data under temporal dependence. Typical examples of non-Euclidean valued time series include yearly mortality distributions, time-varying networks, and covariance matrix time series. To accommodate unknown temporal dependence, the self-normalization (SN) technique is advanced to the inference of non-Euclidean time series, which is substantially different from the existing SN-based inference for functional time series that reside in Hilbert space. Theoretically, new regularity conditions are proposed that could be easier to check than those in the recent literature and derive the limiting distributions of the proposed test statistics under both null and local alternatives. For the change-point detection problem, the consistency for the change-point location estimator is also derived, and the proposed change-point test is combined with wild binary segmentation to perform multiple change-point estimation. Numerical simulations and real data illustrations demonstrate the effectiveness and robustness of the proposed tests compared with existing methods in the literature.
