Statistical inference for piecewise normal distributions and stochastic variational inequalities

Abstract

In this paper we first provide a method to compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution, under certain assumptions. We then extend this method to an asymptotic setting, and apply this method to compute confidence intervals for the true solution of a stochastic variational inequality based on a solution to a sample average approximation problem. The confidence intervals are computed with simple formulas. Performance of the proposed method is tested with numerical experiments.

The computer codes for the numerical examples contain mistakes that cause errors in results for the numerical example at the end of Section 3.3, and the two numerical examples in Section 4