The Asymptotic Validity of Sequential Stopping Rules for Stochastic Simulations

1992/02/01 by Peter W. Glynn, Ward Whitt · 11 citations
Business, Management and Accounting · Decision Sciences · #Advanced Queuing Theory Analysis #Probability and Risk Models #Simulation Techniques and Applications

paper · pdf · doi:10.1214/aoap/1177005777

openalex publication_date 1992/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

We establish general conditions for the asymptotic validity of sequential stopping rules to achieve fixed-volume confidence sets for simulation estimators of vector-valued parameters. The asymptotic validity occurs as the prescribed volume of the confidence set approaches 0. There are two requirements: a functional central limit theorem for the estimation process and strong consistency (with-probability-1 convergence) for the variance or "scaling matrix" estimator. Applications are given for: sample means of i.i.d. random variables and random vectors, nonlinear functions of such sample means, jackknifing, Kiefer-Wolfowitz and Robbins-Monro stochastic approximation and both regenerative and nonregenerative steady-state simulation.

Citations

• On the Asymptotic Theory of Fixed-Width Sequential Confidence Intervals for the Mean

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