Inference on Estimators defined by Mathematical Programming

TL;DR

This paper develops an inference method for estimators derived from mathematical programming problems like LP and QP, accounting for sampling error in estimated coefficients, and demonstrates its effectiveness through simulations and a finance application.

Contribution

It introduces a novel inference approach leveraging complementarity conditions to handle estimation error in LP and QP solutions, transforming the problem into inequality-based inference.

Findings

The proposed method performs well in Monte Carlo simulations.

It provides reliable inference in a portfolio selection application.

The approach effectively accounts for sampling variability in optimization-based estimators.

Abstract

We propose an inference procedure for estimators defined by mathematical programming problems, focusing on the important special cases of linear programming (LP) and quadratic programming (QP). In these settings, the coefficients in both the objective function and the constraints of the mathematical programming problem may be estimated from data and hence involve sampling error. Our inference approach exploits the characterization of the solutions to these programming problems by complementarity conditions; by doing so, we can transform the problem of doing inference on the solution of a constrained optimization problem (a non-standard inference problem) into one involving inference based on a set of inequalities with pre-estimated coefficients, which is much better understood. We evaluate the performance of our procedure in several Monte Carlo simulations and an empirical application to the classic portfolio selection problem in finance.