Open Access
February, 1992 The Asymptotic Validity of Sequential Stopping Rules for Stochastic Simulations
Peter W. Glynn, Ward Whitt
Ann. Appl. Probab. 2(1): 180-198 (February, 1992). DOI: 10.1214/aoap/1177005777


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.


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Peter W. Glynn. Ward Whitt. "The Asymptotic Validity of Sequential Stopping Rules for Stochastic Simulations." Ann. Appl. Probab. 2 (1) 180 - 198, February, 1992.


Published: February, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0792.68200
MathSciNet: MR1143399
Digital Object Identifier: 10.1214/aoap/1177005777

Primary: 68U20
Secondary: 60F17 , 60G40 , 62L12 , 62L15 , 65C05

Keywords: fixed-width confidence intervals , functional central limit theorems , sequential estimation , sequential stopping rules , Stochastic simulation , strong consistency , variance estimators

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.2 • No. 1 • February, 1992
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