Retrospective change-point detection and estimation in multivariate linear models

TL;DR

This paper introduces a new method for retrospective change-point detection in multivariate linear models, providing theoretical bounds, asymptotic optimality, and simulation comparisons with existing methods.

Contribution

A novel retrospective change-point detection method with proven asymptotic optimality and comprehensive performance analysis in multivariate linear models.

Findings

The proposed method achieves asymptotic optimality in change-point estimation.

Simulation results show competitive performance compared to existing methods.

Theoretical bounds for estimation errors are established for various scenarios.

Abstract

In this paper the problem of retrospective change-point detection and estimation in multivariate linear models is considered. The lower bounds for the error of change-point estimation are proved in different cases (one change-point: deterministic and stochastic predictors, multiple change-points). A new method for retrospective change-point detection and estimation is proposed and its main performance characteristics (type 1 and type 2 errors, the error of estimation) are studied for dependent observations in situations of deterministic and stochastic predictors and unknown change-points. We prove that this method is asymptotically optimal by the order of convergence of change-point estimates to their true values as the sample size tends to infinity. Results of a simulation study of the main performance characteristics of proposed method in comparison with other well known methods of retrospective change-point detection and estimation are presented.