Efficient Multiple Change Point Detection and Localization For High-Dimensional Quantile Regression with Heteroscedasticity

Data heterogeneity is a challenging issue for modern statistical data analysis. There are different types of data heterogeneity in practice. In this paper, we consider potential structural changes and complicated tail distributions. There are various existing methods proposed to handle either structural changes or heteroscedasticity. However, it is difficult to handle them simultaneously. To overcome this limitation, we consider statistically and computationally efficient change point detection and localization in high-dimensional quantile regression models. Our proposed framework is general and flexible since the change points and the underlying regression coefficients are allowed to vary across different quantile levels. The model parameters, including the data dimension, the number of change points, and the signal jump size, can be scaled with the sample size. Under this framework, we construct a novel two-step estimation of the number and locations of the change points as well as the underlying regression coefficients. Without any moment constraints on the error term, we present theoretical results, including consistency of the change point number, oracle estimation of change point locations, and estimation for the underlying regression coefficients with the optimal convergence rate. Finally, we present simulation results and an application to the S&P 100 dataset to demonstrate the advantage of the proposed method.