Robust change point detection for linear regression models

Abstract

Linear models incorporating change points are very common in many scientific fields including genetics, medicine, ecology, and finance. Outlying or unusual data points pose another challenge for fitting such models, as outlying data may impact change point detection and estimation. In this paper, we propose a robust approach to estimate the change point/s in a linear regression model in the presence of potential outlying point/s or with non-normal error structure. The statistic that we propose is a partial F statistic based on the weighted likelihood residuals. We examine its asymptotic properties and finite sample properties using both simulated data and in two real data sets.