A0853
Title: Change point detection for high-dimensional linear models: A general tail-adaptive approach
Authors: Bin Liu - School of Management at Fudan University (China) [presenting]
Abstract: The change point detection problem is studied for high-dimensional linear regression models. The existing literature mainly focused on the change point estimation with stringent sub-Gaussian assumptions on the errors. In practice, however, there is no prior knowledge about the existence of a change point or the tail structures of errors. To address these issues, a novel tail-adaptive approach is proposed for simultaneous change point testing and estimation. The method is built on a new loss function, which is a weighted combination between the composite quantile and least squared losses, allowing the borrowing of information on the possible change points from both the conditional mean and quantiles. Under some mild conditions, the validity of the new tests is justified in terms of size and power under the high-dimensional setup. The corresponding change point estimators are shown to be rate optimal up to a logarithm factor. Moreover, combined with the wild binary segmentation technique, a new algorithm is proposed to detect multiple change points in a tail-adaptive manner. Extensive numerical results are conducted to illustrate the appealing performance of the proposed method.
