# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1907.05353