Open Access
June 2021 Factor-driven two-regime regression
Sokbae Lee, Yuan Liao, Myung Hwan Seo, Youngki Shin
Author Affiliations +
Ann. Statist. 49(3): 1656-1678 (June 2021). DOI: 10.1214/20-AOS2017


We propose a novel two-regime regression model where regime switching is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a panel data set. We show that the optimization problem can be reformulated as mixed integer optimization, and we present two alternative computational algorithms. We derive the asymptotic distribution of the resulting estimator under the scheme that the threshold effect shrinks to zero. In particular, we establish a phase transition that describes the effect of first-stage factor estimation as the cross-sectional dimension of panel data increases relative to the time-series dimension. Moreover, we develop bootstrap inference and illustrate our methods via numerical studies.

Funding Statement

We would like to thank the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2018S1A5A2A01033487), the Social Sciences and Humanities Research Council of Canada (SSHRC-435-2018-0275), the European Research Council for financial support (ERC-2014-CoG-646917-ROMIA) and the UK Economic and Social Research Council for research grant (ES/P008909/1) to the CeMMAP.


We would like to thank an Associate Editor and two anonymous referees for helpful comments.


Download Citation

Sokbae Lee. Yuan Liao. Myung Hwan Seo. Youngki Shin. "Factor-driven two-regime regression." Ann. Statist. 49 (3) 1656 - 1678, June 2021.


Received: 1 March 2020; Revised: 1 August 2020; Published: June 2021
First available in Project Euclid: 9 August 2021

MathSciNet: MR4298876
zbMATH: 1475.62175
Digital Object Identifier: 10.1214/20-AOS2017

Primary: 62H25
Secondary: 62F12

Keywords: mixed integer optimization , oracle properties , phase transition , Principal Component Analysis , threshold regression

Rights: Copyright © 2021 Institute of Mathematical Statistics

Vol.49 • No. 3 • June 2021
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