STOR Colloquium: Yuan Liao, Rutgers University
Factor-Driven Two-Regime Regression using
Mixed Integer Programming
We propose a two-regime regression model where the switching between the regimes is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a much larger data set. We show that the optimization problem can be reformulated as mixed integer optimization and present two alternative computational algorithms: (1) MI quadratic programming and (2) MI linear programming. We show that (1) is numerically equivalent to the original least squares problem, but runs slowly. On the other hand, (2) runs much faster, and produces asymptotically equivalent estimators. We derive the asymptotic distributions of the resulting estimators, and establish a phase transition that describes the effect of first stage factor estimation.
The paper can be downloaded from https://arxiv.org/abs/1810.11109