Abstract
Let {V(k) :K⩾1} be a sequence of independent, identically distributed random vectors in ℝd with mean vector μ. The mappingg is a twice differentiable mapping from ℝd to ℝ1. Setr=g(μ). A bivariate central limit theorem is proved involving a point estimator forr and the asymptotic variance of this point estimate. This result can be applied immediately to the ratio estimation problem that arises in regenerative simulation. Numerical examples show that the variance of the regenerative variance estimator is not necessarily minimized by using the “return state” with the smallest expected cycle length.
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References
P. Bratley, B.L. Fox and L. Schrage,A Guide to Simulation (Springer-Verlag, New York, 1983).
B.L. Fox and P.W. Glynn, Conditional Monte Carlo estimators for semi-Markov processes, forthcoming technical report, Mathematics Research Center, University of Wisconsin, Madison, Wisconsin (1985).
P.W. Glynn and D.L. Iglehart, Recursive moment formulas for the regenerative method of simulation, Technical Report No. 29, Department of Operations Research, Stanford University, Stanford, California (1984). To appear in theProc. Int. Symp. on Semi-Markov Processes and their Applications, Brussels.
P.W. Glynn and D.L. Iglehart, A joint central limit theorem for the sample mean and variance of a function of random vector, forthcoming technical report, Department of Operations Research, Stanford University, Stanford, California (1985).
D.L. Iglehart, The regenerative method for simulation analysis, in:Current Trends in Programming Methodology — Software Modeling, ed. K.M. Chandy and R.T. Yeh (Prentice-Hall, Englewood Cliffs, NJ, 1978).
A.M. Law and W.D. Kelton,Simulation Modeling and Analysis (McGraw-Hill, New York, 1982).
W.L. Smith, Regenerative stochastic processes, Proc. Roy. Soc. London Ser. A232(1955)6.
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This research was supported by Army Research Office Contract DAAG29-84-K-0030. The first author was also supported by National Science Foundation Grant ECS-8404809 and the second author by National Science Foundation Grant MCS-8203483.
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Glynn, P.W., Iglehart, D.L. A joint central limit theorem for the sample mean and regenerative variance estimator. Ann Oper Res 8, 41–55 (1987). https://doi.org/10.1007/BF02187081
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DOI: https://doi.org/10.1007/BF02187081