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Symmetric confidence regions and confidence intervals for normal map formulations of stochastic variational inequalities

Shu Lu(shulu***at***email.unc.edu)

Abstract: Stochastic variational inequalities (SVI) model a large class of equilibrium problems subject to data uncertainty, and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation (SAA) problem. This paper considers the normal map formulation of an SVI, and proposes a method to build asymptotically exact con dence regions and con dence intervals for the solution of the normal map formulation, based on the asymptotic distribution of SAA solutions. The con dence regions are single ellipsoids with high probability. We also discuss the computation of simultaneous and individual con dence intervals.

Keywords: con dence region, con dence interval, stochastic variational inequality, sample average approximation, stochastic optimization, normal map

Category 1: Complementarity and Variational Inequalities

Category 2: Stochastic Programming

Citation: Department of Statistics and Operations Research, University of North Carolina at Chapel Hill

Download: [PDF]

Entry Submitted: 06/26/2014
Entry Accepted: 06/26/2014
Entry Last Modified: 06/26/2014

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