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Inference on estimators defined by mathematical programming

Hsieh, Yu-Wei and Shi, Xiaoxia and Shum, Matthew (2022) Inference on estimators defined by mathematical programming. Journal of Econometrics, 226 (2). pp. 248-268. ISSN 0304-4076. doi:10.1016/j.jeconom.2021.06.001.

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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.

Item Type:Article
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URLURL TypeDescription Paper
Shum, Matthew0000-0002-6262-915X
Additional Information:© 2021 Elsevier B.V. Received 5 September 2019, Revised 8 April 2021, Accepted 9 June 2021, Available online 29 June 2021. We thank Denis Chetverikov, Jin-Chuan Duan, Bulat Gafarov, Bryan Graham, Jinyong Hahn, Po-Hsuan Hsu, Yuichi Kitamura, Emerson Melo, Ismael Mourifié, Andres Santos, Yixiao Sun; seminar listeners at Chinese University of Hong Kong, UC-Riverside and UC-San Diego; and attendees at the California Econometrics Conference (10/17), the CeMMAP Conference on Machine Learning and Optimization (3/18), the Rotterdam Workshop on Machine Learning and Causal Inference (5/18), 2018 North American Summer Meeting of the Econometric Society at UC-Davis, and 2018 Taiwan Economic Research Conference for comments.
Subject Keywords:Linear complementarity constraints; Moment inequalities; Sub-vector inference; Portfolio selection
Issue or Number:2
Classification Code:JEL: C10; C12; C63
Record Number:CaltechAUTHORS:20210714-163200205
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Official Citation:Yu-Wei Hsieh, Xiaoxia Shi, Matthew Shum, Inference on estimators defined by mathematical programming, Journal of Econometrics, Volume 226, Issue 2, 2022, Pages 248-268, ISSN 0304-4076,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109811
Deposited By: Tony Diaz
Deposited On:14 Jul 2021 17:28
Last Modified:04 Jan 2022 21:13

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