Simultaneous Change Point Detection and Identification for High Dimensional Linear Models

Bing Liu

<p><span style="font-size: medium;"><span style="font-family: Arial;"><span class="fontstyle0">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 </span><span class="fontstyle2">L</span><span class="fontstyle3">1&nbsp;</span><span class="fontstyle0">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 </span><span class="fontstyle2">L</span><span class="fontstyle3">1</span><span class="fontstyle0">-norm, then a change point estimator is obtained by taking &ldquo;argmax&rdquo; with respect to time of the above aggregated process. Under </span><span class="fontstyle4">H</span><span class="fontstyle5">1</span><span class="fontstyle0">, 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<br /> 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)<br /> </span><span class="fontstyle6">Keyword: </span><span class="fontstyle0">Change point inference; High dimensions; Linear regression; Multiplier bootstrap; Sparsity; Subgroups.</span>&nbsp;&nbsp;</span></span></p>

2020-04-10(Friday)10:00-11:00

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Ming Lin

<p>&nbsp;<span class="fontstyle0">Liu Bin, Postdoctor,</span> &nbsp;The Chinese University of HongKong</p> <p>&nbsp;</p> <p><span class="fontstyle0">Education Background<br /> </span><span class="fontstyle2">? </span><span class="fontstyle3">2009.09--2013.06 Bachelor&rsquo;s degree, Shandong University, Statistics<br /> </span><span class="fontstyle2">? </span><span class="fontstyle3">2013.09--2019.06 PhD, School of Management, Fudan University, Probability and<br /> </span></p> <p><span class="fontstyle3">Mathematical Statistics<br /> </span><span class="fontstyle2">? </span><span class="fontstyle3">2019.07--2020.07 Postdoctor, Department of Statistics, The Chinese University of HongKong<br /> </span><span class="fontstyle0">Overseas exchange experience<br /> </span><span class="fontstyle3">2017.09--2018.09, Department of Statistics, the University of North Carolina at Chapel Hill<br /> </span></p> <p><span class="fontstyle0">Research Interests<br /> </span><span class="fontstyle3">High dimensional inference, Change point analysis, Data-adaptive test, Gaussian<br /> graphical models, U statistics, Gaussian approximations and Bootstrap</span>&nbsp;&nbsp;</p>