Title: Change point inference for high-dimensional correlation matrix
Authors: Zhaoyuan Li - The Chinese University of Hong Kong, Shenzhen (China) [presenting]
Abstract: The focus is on the problem of detecting and estimating a change point in the correlation matrix in a sequence of high dimensional vectors, where the dimension is substantially large compared to the sample size. We first propose a simulation-based approach to detect whether a change point exists or not. When we have witnessed a change point in the first step, a two-stage method is proposed to estimate the location of the change point. The first step consists of a reduction of the dimension to identify elements of the correlation matrices corresponding to significant changes, where the threshold is generated by a simulation-based procedure. In the second step, we use the components after dimension reduction to determine the position of the change point. This method can efficiently estimate not only the change point located in the middle of the sequence, but also that located at the tails, which will be very useful for online detection. Theoretical properties are developed for both approaches, and numerical studies are conducted to support the new methodology.