报告题目：Change Point Inference for High Dimensional Linear Models
主 讲 人：刘彬
报告地点：腾讯会议 会议 ID：217 991 811
Heterogeneity is a challenging problem for large scale data sequences in modern statistical applications, where parameters of the data-generating process may undergo sudden changes at a possible but unknown time point. In this article, we consider simultaneous change point detection and identification in the context of high dimensional linear models. For change point detection, given any subgroup of variables, we propose a new method for testing the homogeneity of corresponding regression coefficients across the observations. The test statistic is based on a weighted L_\infinity aggregation, both temporally and spatially, of a de-biased lasso process. A multiplier bootstrap procedure is introduced to approximate its limiting distribution. It is shown that the proposed bootstrap automatically accounts for the covariance structures of the de-biased lasso process and allows the number of variables to grow exponentially with the sample size. Furthermore, under some regularity conditions, the proposed new testing procedure controls the type I error asymptotically and is powerful against sparse alternatives and enjoys certain optimality. For change point identification, at each fixed time point, we first aggregate spatial information of the de-biased lasso process with the L_\infinity-norm, then a change point estimator is obtained by taking “argmax” with respect to time of the above aggregated process. Under H1, the change point estimator is shown to be consistent for the true change point location. To further improve the estimation accuracy of change point estimators, a novel two-step refitting-based algorithm is proposed. Moreover, combining with the binary segmentation technique, we further extend our new method for detecting and identifying multiple change points. Extensive simulation studies justify the validity of our new method and analysis of a dataset from the Alzheimer’s Disease Neuroimaging Initiative further demonstrates its competitive performance.
刘彬，复旦大学管理学院统计系助理教授。刘彬博士本科毕业于山东大学，在复旦大学管理学院获理学博士学位，并在香港中文大学统计系进行为期一年的博士后研究。刘彬博士的主要研究方向为高维统计推断，变点分析，数据趋动检验，高斯逼近及Bootstrap，稳健方法等，并在 JRSSB，JMVA以及Australian & New Zealand Journal of Statistics 等统计期刊发表多篇有影响力的论文。