A1362
Title: Efficient oracle-based estimation and inference for multiple change points in high-dimensional Gaussian graphical models
Authors: Xianru Wang - Southwestern University of Finance and Economics (China) [presenting]
Abstract: Efficient multiple change point estimation and inference for high-dimensional Gaussian Graphical Models (GGMs) under temporal dependence is studied by leveraging nodewise Lasso for graph structure estimation. A two-step procedure and computationally efficient algorithm, the Refined Wild Binary Segmentation (RWBS), are proposed for detecting and refining multiple change points. Additionally, a practical procedure for confidence interval construction for change point locations is developed. Under mild model assumptions, theoretical guarantees for the proposed algorithm are established, including consistency in estimating the number of change points, oracle-level accuracy in locating change points, and favorable convergence rates for the underlying coefficient vectors. The methodology is extended to accommodate temporally dependent observations by introducing a formal dependence structure and deriving corresponding probabilistic guarantees. Extensive numerical studies and an application to the S\&P 500 dataset demonstrate the computational efficiency and statistical accuracy of the proposed method.
