  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.
