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.
@article{1177005777,
author = {Glynn, Peter W. and Whitt, Ward},
title = {The Asymptotic Validity of Sequential Stopping Rules for Stochastic Simulations},
journal = {Ann. Appl. Probab.},
volume = {2},
number = {4},
year = {1992},
pages = { 180-198},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005777}
}
Glynn, Peter W.; Whitt, Ward. The Asymptotic Validity of Sequential Stopping Rules for Stochastic Simulations. Ann. Appl. Probab., Tome 2 (1992) no. 4, pp. 180-198. http://gdmltest.u-ga.fr/item/1177005777/