Factor-driven two-regime regression

Sokbae Lee, Yuan Liao, Myung Hwan Seo, Youngki Shin

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1656-1678
Number of pages23
JournalAnnals of Statistics
Issue number3
StatePublished - Jun 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Mixed integer optimization
  • Oracle properties
  • Phase transition
  • Principal component analysis
  • Threshold regression


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