Abstract
Threshold bootstrap is a modified bootstrap method that resamples data from the autocorrelated simulation outputs. The threshold bootstrap calculate the ensemble average of sample as an estimator for population mean as do other bootstrap methods. Sometimes, however, an estimator of simulation output is generated by the concept of time average such as mean queue size in queueing system. In this situation, to analyze the simulation output more efficiently, we introduce a method of generating the confidence intervals for time averaged estimators using the threshold bootstrap. Numerical examples are provided to verify the confidence interval produced by our method.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Efron, B.: Bootstrap Methods: Another Look at the jackknife. The Annals of Statistics 7, 1–26 (1979)
Efron, B., Tibshirani, R.: Bootstrap Methods for Standard Errors, Confidence Intervals and Other Measures of Statistical Accuracy. Statistical Science 1, 54–75 (1986)
Melamed, B., Whitt, W.: On Arrivals that See Time Averages: A martingale Approach. Journal of Applied Probability 27, 376–384 (1990)
Kim, Y.B., Whillemain, T.R., Haddock, J., Runger, G.C.: The threshold bootstrap: a new approach to simulation output analysis. In: Proceedings of the 1993 Winter Simulation Conference, pp. 498–502 (1993)
Kùnsch, H.R.: The jackknife and the bootstrap for general stationary observations. Annals of Statistics 17, 1217–1241 (1989)
Liu, R., Singh, K.: Moving blacks jackknife and bootstrap capture weak dependence. In: Lepage, R., Billard, L. (eds.) Exploring the Limits of Bootstrap, pp. 225–248. Willey, New York (1992)
Park Dae, S., Kim, Y.B., Shin, K.I., Willemain, T.R.: Simulation output analysis using the threshold bootstrap. European Journal of Operational Research 134, 17–28 (2001)
Daesu, P., Willemain, T.R.: The threshold bootstrap and threshold jackknife. Computational Statistics & Data Analysis 31, 187–202 (1999)
Hall, P., Horowitz, J.L., Jing, B.-Y.: On blocking rules for the bootstrap with dependent data. Biometrika 82(3), 561–574 (1995)
Hall, P., Jing, B.: On Sample Reuse Methods for Dependent Data. Journal of the Royal Statistical Society 58(4), 727–737 (1996)
Politis, D.N., Romano, J.P.: The Stationary Bootstrap. Journal of American Statistics Association 89, 1303–1313 (1994)
Wolff, R.W.: Poisson Arrivals See Time Averages. Operations Research 30, 223–231 (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Park, J. et al. (2013). Generating the Confidence Interval of Time Averaged Estimator Using Threshold Bootstrap. In: Tan, G., Yeo, G.K., Turner, S.J., Teo, Y.M. (eds) AsiaSim 2013. AsiaSim 2013. Communications in Computer and Information Science, vol 402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45037-2_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-45037-2_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45036-5
Online ISBN: 978-3-642-45037-2
eBook Packages: Computer ScienceComputer Science (R0)