A new method to build confidence regions for solutions of stochastic variational inequalities

Abstract

Stochastic variational inequalities model a large class of equilibrium problems subject to data uncertainty. The true solution to such a problem is usually estimated by a solution to its sample average approximation (SAA) problem. This article proposed a new method to build asymptotically exact confidence regions for the true solution that are computable from the SAA solution.

Keywords:

• variational inequality
• stochastic variational inequality
• confidence regions
• statistical inference
• sample average approximation

AMS Subject Classifications::

• 90C33
• 90C15

Acknowledgements

This research was supported by National Science Foundation under grants DMS-0807893 and DMS-1109099. The author thanks Professor Stephen M. Robinson for introducing her to this subject.