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Activity Number: 412 - Theory and Methods for Change-Point and Abnormality Detection
Type: Contributed
Date/Time: Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #329117 Presentation
Title: Finite Sample Change Point Inference and Identification for Hig-Dimensional Mean Vectors
Author(s): Mengjia Yu* and Xiaohui Chen
Companies: University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
Keywords: high-dimensional data; change point analysis; CUSUM; Gaussian multiplier bootstrap
Abstract:

We studied two problems for high-dimensional change point inference and identification in mean vectors based on the supremum norm of the CUSUM statistics with a boundary removal parameter. For the problem of testing for existence of a mean-shift in a sequence of independent observations, we introduce a Gaussian multiplier bootstrap to approximate the critical values of the CUSUM test statistics when dimension $p$ is much larger than $n$. Under arbitrary dependence structures and mild moment conditions, our test enjoys the uniform validity in size under the null and is powerful under the sparse alternatives. Once a change point is detected, the location is estimated by maximizing the sup-norm of generalized CUSUM statistics at two different weighting scales. In both of the estimators that relied on the covariance stationary CUSUM statistics and the non-stationary one with less weights on boundary points, consistency is achieved in possible optimal rate of $n$ for sub-exponential case up to a log factor, only through which $p$ impacts the convergence rate. The results are non-asymptotic, data-dependent and simulations in finite samples show an encouraging agreement with theoretics.


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