Dating the Break in High-dimensional Data

Detecting and dating structural breaks in functional data without dimension reduction

Methodology is proposed to uncover structural breaks in functional data that is "fully functional" in the sense that it does not rely on dimension reduction techniques. A thorough asymptotic theory is developed for a fully functional break detection procedure as well as for a break date estimator, assuming a fixed break size and a shrinking break size. The latter result is utilized to derive confidence intervals for the unknown break date. The main results highlight that the fully functional procedures perform best under conditions when analogous fPCA based estimators are at their worst, namel…

Testing and Dating Structural Changes in Copula-based Dependence Measures

This paper is concerned with testing and dating structural breaks in the dependence structure of multivariate time series. We consider a cumulative sum (CUSUM) type test for constant copula-based dependence measures, such as Spearman's rank correlation and quantile dependencies. The asymptotic null distribution is not known in closed form and critical values are estimated by an i.i.d. bootstrap procedure. We analyze size and power properties in a simulation study under different dependence measure settings, such as skewed and fat-tailed distributions. To date break points and to decide whether…

Modeling Multivariate Cyber Risks: Deep Learning Dating Extreme Value Theory

Modeling cyber risks has been an important but challenging task in the domain of cyber security. It is mainly because of the high dimensionality and heavy tails of risk patterns. Those obstacles have hindered the development of statistical modeling of the multivariate cyber risks. In this work, we propose a novel approach for modeling the multivariate cyber risks which relies on the deep learning and extreme value theory. The proposed model not only enjoys the high accurate point predictions via deep learning but also can provide the satisfactory high quantile prediction via extreme value theo…

Hypothesis Testing for High-Dimensional Multinomials: A Selective Review

The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional multinomials. Traditional tests like the $χ^2$ test and the likelihood ratio test can have poor power in the high-dimensional setting. Much of the research in this area has focused on finding tests with asymptotically Normal limits and developing (stringent) conditions under which tests have Normal limits. We argue that this perspective suffers from a significan…

无限维转移概率矩阵的估计：基于广义层次化断棍过程

Estimation of An Infinite Dimensional Transition Probability Matrix Using a Generalized Hierarchical Stick-Breaking Process

本文提出广义层次化断棍先验的贝叶斯非参数框架，用于估计无限维转移概率矩阵，应对稀疏、高维及未观测状态空间挑战。

高维函数型时间序列中结构突变点的检测与估计

Detection and Estimation of Structural Breaks in High-Dimensional Functional Time Series

本文针对高维函数型时间序列提出融合函数型CUSUM与功效增强分量的突变点检验方法，并通过潜在组结构聚类算法一致估计异质性突变点及组归属，从而提升突变点估计的收敛性能。