Mathematica notebook for h-statistics based MC and MLMC covariance estimation

This repository contains a Mathematica notebook which lists and generates equations related to h-statistics based Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) covariance estimation using the mathStatica library.

The notebook provided here serves as supplementary material for the article titled "S. Shivanand. Covariance estimation using h-statistics in Monte Carlo and multilevel Monte Carlo methods. arXiv, 2023.", which can be found here.

Contents

• h_statistics_covariance_estimation.nb: Mathematica notebook containing the equations for h-statistics based MC and MLMC covariance estimation.

Requirements

To run the notebook, you need:

• Mathematica software installed on your system.
• The mathStatica library.

Usage

1. Open the h_statistics_covariance_estimation.nb notebook in Mathematica.
2. Follow the instructions within the notebook to generate equations for h-statistics based MC and MLMC covariance estimation.

Citation

If you find this notebook or the associated article useful, please consider citing:

@article{Shivanand2023hstatcov,
author = S.Shivanand,
title = Covariance estimation using h-statistics in Monte Carlo and multilevel Monte Carlo
methods,
archivePrefix={arXiv},
year = {2023},
doi = {https://doi.org/10.48550/arXiv.2311.01336},
eprint = {arXiv:2311.01336},
primaryClass={math.ST}
}