Work

Change Point Detection for High-dimensional Linear Models: A General Tail-adaptive Approach

Year: 2024

Type: article

Abstract: We propose a novel approach for detecting change points in highdimensional linear regression models.Unlike previous research that relies on strict Gaussian/sub-Gaussian error assumptions and has prior knowledge of change points, we propose a tail-adaptive method for change point detection and estimation.We use a weighted combination of composite quantile and least squared losses to build a new loss function, allowing us to leverage information from both conditional means and quantiles.For change point testing, we develop a family of individual testing statistics with different weights to account for unknown tail structures.These individual tests are further aggregated to construct a powerful tail-adaptive test for sparse regression coefficient changes.For change point estimation, we propose a family of argmax-based individual estimators.We provide theoretical justifications for the validity of these tests and change point estimators.Additionally, we introduce a new algorithm for detecting multiple change points in a tail-adaptive manner using the wild binary segmentation.

Source: Statistica Sinica

DOI: 10.5705/ss.202023.0337

Authors: Bin Liu, Zhengling Qi, Xinsheng Zhang, Yufeng Liu

Institutions: George Washington University, Fudan University, University of North Carolina at Chapel Hill

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Natural Science Foundation of China

Awards: G4766654764, G5678262830