Statistical inference for piecewise normal distributions and stochastic variational inequalities
Optimization and Control
2022-08-08 v2 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.1907.05353,
title = {Statistical inference for piecewise normal distributions and stochastic variational inequalities},
author = {Shu Lu and Hongsheng Liu},
journal= {arXiv preprint arXiv:1907.05353},
year = {2022}
}
Comments
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