Denis Choquet
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Abstract
We are concerned with computing a confidence interval for the ratio E[Y]/E[X, where (X,Y) is a pair of random variables. This ratio estimation problem arises in, for instance, regenerative simulation. As an alternative to confidence intervals based on asymptotic normality, we study and compare different variants of the bootstrap for one-sided and two-sided intervals. We point out situations where these techniques provide confidence intervals with coverage much closer to the nominal value than do the classical methods.
- ASMUSSEN, S. 1987. Applied Probability and Queues. John Wiley and Sons, Inc., New York, NY.Google Scholar
- CHANG, C.-S., HEIDELBERGER, P., JUNEJA, S., AND SHAHABUDDIN, P. 1994. Effective bandwidth and fast simulation of ATM intree networks. Perform. Eval. 20, 1-3 (May 1994), 45-65. Google Scholar
- CHENG, R. C. H. 1995. Bootstrap methods in computer simulation experiments. In Proceedings of the 1995 Winter Conference on Simulation (WSC '95, Arlington, VA, Dec. 3-6), W. R. Lilegdon, D. Goldsman, C. Alexopoulos, and K. Kang, Eds. ACM Press, New York, NY, 171-177. Google Scholar
- CHOQUET, D. 1997. Intervalles de confiance bootstrap pour la simulation de processus regeneratifs. Master's Thesis. Univ. de Montreal, Monreal, Canada.Google Scholar
- CRANE, M. A. AND IGLEHART, D. L. 1974. Simulating stable stochastic systems, I: General mutiserver queues. J. ACM 21, 1 (Jan.), 103-113. Google Scholar
- DAVISON, A. C. AND HINKLEY, D.V. 1997. Bootstrap Methods and Their Application. Cambridge University Press, New York, NY.Google Scholar
- EFRON, B. 1979. Bootstrap methods: Another look at the jackknife. Ann. Stat. 7, 1-26.Google Scholar
- EFRON, B. AND TIBSHIRANI, R.J. 1993. An Introduction to the Bootstrap. Chapman & Hall, London, UK.Google Scholar
- FIELLER, E. 1954. Some problems in interval estimation. J. Royal Stat. Soc. B. 16, 175-185.Google Scholar
- FISHMAN, G. S. 1973. Concepts and Methods in Discrete Event Digital Simulation. John Wiley and Sons, Inc., New York, NY.Google Scholar
- Fox, B. L. AND GLYNN, P.W. 1989. Simulating discounted costs. Manage. Sci. 35, 11 (Nov. 1989), 1297-1315. Google Scholar
- GLASSERMAN, P. 1991. Gradient Estimation Via Perturbation Analysis. Kluwer Academic Publishers, Hingham, MA.Google Scholar
- GLYNN, P. W., L'ECUYER, P., AND AD S, M. 1991. Gradient estimation for ratios. In Proceedings of the Winter Conference on Simulation (Piscataway, NJ), B. L. Nelson, W. D. Kelton, and G. M. Clark, Eds. IEEE Press, Piscataway, NJ, 986-993. Google Scholar
- HALL, P. 1986. On the number of bootstrap simulations required to construct a confidence interval. Ann. Stat. 14, 1453-1462.Google Scholar
- HALL, P. 1988. Theoretical comparison of bootstrap confidence intervals. Ann. Stat. 16, 927-985.Google Scholar
- HALL, P. 1992. The Bootstrap and Edgeworth Expansion. Springer-Verlag, New York, NY.Google Scholar
- HWANG, J. T. G. 1995. Fieller's problems and resampling techniques. Stat. Sinica 5, 161-171.Google Scholar
- IGLEHART, D. L. 1975. Simulating stable stochastic systems V: Comparison of ratio estimators. Naval Res. Logistics Q. 22, 553-565.Google Scholar
- LAW, A. AND KELTON, W. 1991. Simulation Modeling and Analysis. 2nd. ed. McGraw-Hill, Inc., New York, NY. Google Scholar
- L'ECUYER, P. 1990. A unified view of the IPA, SF, and LR gradient estimation techniques. Manage. Sci. 36, 11 (Nov. 1990), 1364-1383. Google Scholar
- L'ECUYER, P. 1991. An overview of derivative estimation. In Proceedings of the Winter Conference on Simulation (Piscataway, NJ), B. L. Nelson, W. D. Kelton, and G. M. Clark, Eds. IEEE Press, Piscataway, NJ, 207-217. Google Scholar
- L'ECUYER, P. AND CHAMPOUX, Y. 1996. Importance sampling for large ATM-type queueing networks. In Proceedings of the Winter Conference on Simulation (WSC '96, Coronado, CA, Dec. 8-11), J. M. Charnes, D. J. Morrice, D. T. Brunner, and J. J. Swain, Eds. ACM Press, New York, NY, 309-316. Google Scholar
- L'ECUYER, P. AND YIN, G. 1998. Budget-dependent convergence rate for stochastic approximation. SIAM J. Optim. 8, 1, 217-247. Google Scholar
- L GER, C., ROMANO, J. P., AND POLITIS, D. N. 1992. Bootstrap technology and applications. Technometrics 34, 4 (Nov. 1992), 378-398. Google Scholar
- MEYN, A. AND TWEEDIE, R. L. 1993. Markov Chains and Stochastic Stability. Springer-Verlag, New York, NY.Google Scholar
- NICOLA, V. F., HAGESTEIJN, G. A., AND KIM, B. G. 1994. Fast simulation of the leaky bucket algorithm. In Proceedings of the 1994 Winter Conference on Simulation (WSC'94, Lake Buena Vista, FL, Dec. 11-14), D. A. Sadowski, A. F. Seila, M. S. Manivannan, and J. D. Tew, Eds. Society for Computer Simulation, San Diego, CA, 266-273. Google Scholar
- RUBINSTEIN, R. Y. AND SHAPIRO, n. 1993. Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method. John Wiley and Sons, Inc., New York, NY.Google Scholar
- SERFLING, R.J. 1980. Approximation Theorems of Mathematical Statistics. John Wiley and Sons, Inc., New York, NY.Google Scholar
- SHAO, J. AND TU, D. 1995. The Jackknife and Bootstrap. Springer-Verlag, New York, NY.Google Scholar
- SHIUE, W. -K., Xu, C. -W., AND REA, C. B. 1993. Bootstrap confidence intervals for simulation outputs. J. Stat. Comput. Simul. 45, 249-255.Google Scholar
- WOLFF, R. W. 1989. Stochastic Modeling and the Theory of Queues. Prentice-Hall, New York, NY.Google Scholar
Index Terms
- Bootstrap confidence intervals for ratios of expectations
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