Inference for change points in high-dimensional data via selfnormalization

This article considers change-point testing and estimation for a sequence of high-dimensional data. In the case mean shift independent data, we propose new test which is based on U-statistic in Chen Qin (Ann. Statist. 38 (2010) 808–835) utilizes self-normalization principle (Shao J. R. Stat. Soc. Ser. B. Methodol. 72 343–366; Shao Zhang Amer. Assoc. 105 1228–1240). Our targets dense alternatives setting involves no tuning parameters. To extend to time series, introduce trimming parameter formulate self-normalized statistic with accommodate weak temporal dependence. On theory front derive limiting distributions statistics under both null dependent At core our asymptotic theory, obtain convergence sequential process trimmed processes linear processes, are interests. Additionally, illustrate how tests can be used combination wild binary segmentation estimate number location multiple change points. Numerical simulations demonstrate competitiveness proposed procedures comparison several existing methods literature.