Computation and analysis of change points with different jump locations in high-dimensional regression

• Published in: Statistical papers (Berlin, Germany) Vol. 65; no. 3; pp. 1703 - 1729
• Main Authors: Huang, Jian, Jiao, Yuling, Kang, Lican, Liu, Yanyan, Yang, Xinfeng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2024; Springer Nature B.V
• Subjects: Algorithms; Dynamic programming; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Insurance; Management; Mathematics and Statistics; Operations Research/Decision Theory; Parameters; Probability Theory and Stochastic Processes; Regression analysis; Regular Article; Sparsity; Statistics; Statistics for Business; Heterogeneity; Change point; Sparsity; Oracle property; Convergence
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-023-01461-w

The purpose of this paper is to study multiple structural changes that occur at unknown locations in high-dimensional linear regression. We consider a structural change model where the parameters are subject to shifts at possibly different locations. We propose a penalized least squares approach, combined with a temporal difference penalty term for the difference between the coefficients at successive points for identifying latent change points, as well as a common sparsity penalty to detect important covariates. This procedure automatically estimates the number and the locations of the change-points and the parameters in each corresponding segment. To implement the proposed approach, we devise an alternating direction method of multipliers (ADMM) algorithm. We demonstrate the convergence of the proposed ADMM algorithm in the present setting. We also establish an oracle inequality for the proposed estimator. We carry out simulation studies to evaluate the finite sample performance of the proposed method and illustrate its application on a data set.