Sequential change point detection for high-dimensional data using nonconvex penalized quantile regression.

In this paper, a sequential change point detection method is developed to monitor structural change in smoothly clipped absolute deviation (SCAD) penalized quantile regression (SPQR) models. The asymptotic properties of the test statistic are derived from the null and alternative hypotheses. In order to improve the performance of the SPQR method, we propose a post-SCAD penalized quantile regression estimator (P-SPQR) for high-dimensional data. We examined the finite sample properties of the proposed methods via Monte Carlo studies under different scenarios. A real data application is provided to demonstrate the effectiveness of the method.