  The sample average approximation (SAA) and the stochastic approximation (SA)
are two popular schemes for solving the stochastic variational inequalities
problem (SVIP). In the past decades, theories on the consistency of the SAA
solutions and SA solutions have been well studied. More recently, the
asymptotic confidence regions of the true solution to SVIP have been
constructed when the SAA scheme is implemented. It is of fundamental interest
to develop confidence regions of the true solution to the SVIP when the SA
scheme is employed. In this paper, we discuss the framework of constructing
asymptotic confidence regions for the true solution of SVIP with a focus on
stochastic dual average method. We first establish the asymptotic normality of
the SA solutions both in ergodic sense and non-ergodic sense. Then the online
methods of estimating the covariance matrices in the normal distributions are
studied. Finally, practical procedures of building the asymptotic confidence
regions of solutions to SVIP with numerical simulations are presented.
