Simultaneous Change Point Detection and Identification for High Dimensional Linear Models

 Liu Bin, Postdoctor,  The Chinese University of HongKong

Education Background
? 2009.09--2013.06 Bachelor’s degree, Shandong University, Statistics
? 2013.09--2019.06 PhD, School of Management, Fudan University, Probability and

Mathematical Statistics
? 2019.07--2020.07 Postdoctor, Department of Statistics, The Chinese University of HongKong
Overseas exchange experience
2017.09--2018.09, Department of Statistics, the University of North Carolina at Chapel Hill

Research Interests
High dimensional inference, Change point analysis, Data-adaptive test, Gaussian
graphical models, U statistics, Gaussian approximations and Bootstrap  

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 L1 aggregation, both temporally and spatially, of a de-biased lasso process. A multiplier bootstrap procedure is introduced to approximate its limiting distribution. For change point identification, at each fixed time point, we first aggregate spatial information of the debiased lasso process with L1-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. Moreover, to further improve the estimation accuracy of change point estimators and reduce the computational burden of the testing procedure, a two-step refitting algorithm and a screeningbased method are proposed. Extensive simulation studies justify the validity of our new
method and a real data application further demonstrates its competitive performance. This is a joint work with Professor Xinsheng Zhang (Fudan University) and Yufeng Liu (UNC)
Keyword: Change point inference; High dimensions; Linear regression; Multiplier bootstrap; Sparsity; Subgroups.