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A Branch-and-Bound Algorithm for Instrumental Variable Quantile Regression

Guanglin Xu (guanglin-xu***at***uiowa.edu)
Samuel Burer (samuel-burer***at***uiowa.edu)

Abstract: This paper studies a statistical problem called instrumental variable quantile regres- sion (IVQR). We model IVQR as a convex quadratic program with complementarity constraints and—although this type of program is generally NP-hard—we develop a branch-and-bound algorithm to solve it globally. We also derive bounds on key vari- ables in the problem, which are valid asymptotically for increasing sample size. We compare our method with two well known global solvers, one of which requires the computed bounds. On random instances, our algorithm performs well in terms of both speed and robustness.

Keywords: Convex quadratic programming; complementarity constraints; branch-and- bound; quantile regression

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Quadratic Programming )

Category 3: Applications -- Science and Engineering (Statistics )


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Entry Submitted: 08/01/2014
Entry Accepted: 08/01/2014
Entry Last Modified: 01/13/2016

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