A0804
Title: Inference on the change point under a high dimensional covariance shift
Authors: Abhishek Kaul - Washington State University (United States) [presenting]
Abstract: The focus is on the problem of constructing asymptotically valid confidence intervals for the change point in a high-dimensional covariance shift setting. A novel estimator for the change point parameter is developed, and its asymptotic distribution under high dimensional scaling is obtained. First, it is established that the proposed estimator exhibits a sharp convergence rate. Further, the form of the asymptotic distributions under both a vanishing and a non-vanishing regime of the jump size is characterized. In the former case, it corresponds to the argmax of an asymmetric Brownian motion, while in the latter case to the argmax of an asymmetric random walk. The relationship between these distributions is then obtained, which allows the construction of regime (vanishing vs non-vanishing) adaptive confidence intervals. Easy-to-implement algorithms for the proposed methodology are developed, and their performance is illustrated on synthetic and real data sets.
