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

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Structural changes in statistical models require robust detection methods.
• Penalized quantile regression, particularly SCAD-penalized quantile regression (SPQR), is effective for high-dimensional data.
• Existing methods may have limitations in sequential monitoring of structural changes.

Purpose of the Study:

• To develop a sequential change point detection method for SPQR models.
• To propose an improved post-SCAD penalized quantile regression (P-SPQR) estimator for high-dimensional settings.
• To evaluate the performance of the proposed methods through simulations and a real data application.

Main Methods:

• Development of a sequential change point detection test statistic for SPQR models.
• Derivation of asymptotic properties for the test statistic under null and alternative hypotheses.
• Introduction of a post-SCAD penalized quantile regression (P-SPQR) estimator designed for high-dimensional data.
• Monte Carlo simulations to assess finite sample properties under various scenarios.

Main Results:

• The proposed sequential change point detection method effectively monitors structural changes in SPQR models.
• The P-SPQR estimator demonstrates improved performance, especially in high-dimensional data.
• Simulation studies confirm the reliability and effectiveness of the developed methods across different scenarios.
• A real-world data application validates the practical utility of the proposed approach.

Conclusions:

• The developed sequential change point detection method offers a valuable tool for analyzing SPQR models.
• The P-SPQR estimator provides a robust solution for structural change detection in high-dimensional data.
• The findings highlight the practical applicability and effectiveness of the proposed statistical methods.