Inference on Estimators Defined by Mathematical Programming
27 Pages Posted: 22 Sep 2017 Last revised: 23 Oct 2018
Date Written: October 21, 2018
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
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