Statistical inference for piecewise normal distributions and stochastic variational inequalities

TL;DR

This paper introduces a simple method for constructing confidence intervals for the centers of piecewise normal distributions and applies it to estimate solutions of stochastic variational inequalities, validated through numerical experiments.

Contribution

It develops a novel, straightforward approach for confidence interval computation in piecewise normal distributions and extends it to stochastic variational inequalities.

Findings

Effective confidence interval formulas demonstrated

Method performs well in numerical tests

Applicable to stochastic variational inequality solutions

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.