Inference on estimators defined by mathematical programming

Yu-Wei Hsieh, Xiaoxia Shi and Matthew Shum

Journal of Econometrics, 2022, vol. 226, issue 2, 248-268

Abstract: We propose an inference procedure for a class of estimators defined as the solutions to linear and convex quadratic programming problems in which the coefficients in both the objective function and the constraints of the problem are estimated from data and hence involve sampling error. We argue 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 solution 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: Linear complementarity constraints; Moment inequalities; Sub-vector inference; Portfolio selection (search for similar items in EconPapers)
JEL-codes: C10 C12 C63 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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Working Paper: Inference on Estimators defined by Mathematical Programming (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:226:y:2022:i:2:p:248-268

DOI: 10.1016/j.jeconom.2021.06.001

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