Statistics and Its Interface

Volume 12 (2019)

Number 2

Robust change point detection for linear regression models

Pages: 203 – 213



Aylin Alin (Department of Statistics, Dokuz Eylul University, Izmir, Turkey)

Ufuk Beyaztas (Department of Statistics, Bartin University, Bartin, Turkey)

Michael A. Martin (Research School of Finance, Actuarial Studies and Statistics, Australian National University, Canberra, ACT, Australia)


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.


bootstrap, Hellinger distance, simple linear regression, robustness, weighted likelihood

2010 Mathematics Subject Classification

62G09, 62G35, 62J05

Received 10 April 2018

Published 11 March 2019