Stopping Rules for Monte Carlo Methods of Martingale Difference Type

TL;DR

This paper develops practical sequential stopping rules for Monte Carlo estimation of non-iid martingale differences, improving implementation and reliability in finite samples with demonstrated numerical effectiveness.

Contribution

It introduces a new, easy-to-implement stopping rule for martingale CLT-based Monte Carlo methods, addressing non-asymptotic challenges and comparing with asymptotic schemes.

Findings

Proposed stopping rules improve reliability in finite samples.

Numerical results show effectiveness in terms of complexity and accuracy.

Framework applicable to various domains.

Abstract

We establish a practical and easy-to-implement sequential stopping rule for the martingale central limit theorem, focusing on Monte Carlo methods for estimating the mean of a non-iid sequence of martingale difference type. Starting with an impractical scheme based on the standard martingale central limit theorem, we progressively address its limitations from implementation perspectives in the non-asymptotic regime. Along the way, we compare the proposed schemes with their counterparts in the asymptotic regime. The developed framework has potential applications in various domains. Numerical results are provided to demonstrate the effectiveness of the developed stopping rules in terms of reliability and complexity.