Inference on Estimators Defined by Mathematical Programming

27 Pages Posted: 22 Sep 2017 Last revised: 23 Oct 2018

See all articles by Yu-Wei Hsieh

Yu-Wei Hsieh

University of Southern California - Department of Economics; USC Dornsife Institute for New Economic Thinking

Xiaoxia Shi

University of Wisconsin - Madison; Yale University

Matthew Shum

California Institute of Technology

Multiple version iconThere are 2 versions of this paper

Date Written: October 21, 2018

Abstract

We propose an inference procedure for estimators defined as the solutions to stochastic mathematical programming problems, in which the coefficients in both the objective function and the constraints of the problem may be estimated from data and hence involve sampling error. We show that the Karush-Kuhn-Tucker conditions that characterize the solutions to these programming problems can be treated as moment conditions; by doing so, we transform the problem of inference on the solution to a constrained optimization problem (which is non-standard) into one involving inference on inequalities with pre-estimated coefficients, which is better understood. Our approach is valid regardless of whether the problem has a unique or multiple solutions. We apply our method to various portfolio selection models, in which the confidence sets can be non- convex, lower-dimensional manifolds.

Keywords: Stochastic Mathematical Programming, Linear Complementarity Constraints, Moment Inequality, Primal-Dual Methods, Sub-Vector Inference, Portfolio Selection

JEL Classification: C10, C12, C63

Suggested Citation

Hsieh, Yu-Wei and Shi, Xiaoxia and Shum, Matthew, Inference on Estimators Defined by Mathematical Programming (October 21, 2018). Available at SSRN: https://ssrn.com/abstract=3041040 or http://dx.doi.org/10.2139/ssrn.3041040

Yu-Wei Hsieh

University of Southern California - Department of Economics ( email )

3620 South Vermont Ave. Kaprielian (KAP) Hall, 300
Los Angeles, CA 90089
United States

USC Dornsife Institute for New Economic Thinking ( email )

3620 S. Vermont Avenue, KAP 364F
Los Angeles, CA 90089-0253
United States

Xiaoxia Shi

University of Wisconsin - Madison ( email )

1180 Observatory Drive
Madison, WI 53706
United States

Yale University

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

Matthew Shum (Contact Author)

California Institute of Technology ( email )

Pasadena, CA 91125
United States

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