omrp.bib

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@ARTICLE{Alexopoulos01012007,
  author = {Alexopoulos, C. and Argon, N. T. and Goldsman, D. and Steiger, N.
	M. and Tokol, G. and Wilson, J. R.},
  title = {Efficient computation of overlapping variance estimators for simulation},
  journal = {INFORMS Journal on Computing},
  year = {2007},
  volume = {19},
  pages = {314-327},
  number = {3},
  abstract = {For a steady-state simulation output process, we formulate efficient
	algorithms to compute certain estimators of the process variance
	parameter (i.e., the sum of covariances at all lags), where the estimators
	are derived in principle from overlapping batches separately and
	then averaged over all such batches. The algorithms require order-of-sample-size
	work to evaluate overlapping versions of the area and Cramer-von
	Mises estimators arising in the method of standardized time series.
	Recently, Alexopoulos et al. showed that, compared with estimators
	based on nonoverlapping batches, the estimators based on overlapping
	batches achieve reduced variance while maintaining similar bias asymptotically
	as the batch size increases. We provide illustrative analytical and
	Monte Carlo results for M/M/1 queue waiting times and for a first-order
	autoregressive process. We also present evidence that the asymptotic
	distribution of each overlapping variance estimator can be closely
	approximated using an appropriately rescaled chi-squared random variable
	with matching mean and variance.}
}

@ARTICLE{Alexopoulos2007,
  author = {Alexopoulos, C. and Argon, N. T. and Goldsman, D. and Tokol, G. and
	Wilson, J. R.},
  title = {Overlapping Variance Estimators for Simulation},
  journal = {Operations Research},
  year = {2007},
  volume = {55},
  pages = {1090-1103},
  number = {6},
  abstract = {To estimate the variance parameter (i.e., the sum of covariances at
	all lags) for a steady-state simulation output process, we formulate
	certain statistics that are computed from overlapping batches separately
	and then averaged over all such batches. We form overlapping versions
	of the area and Cramer-von Mises estimators using the method of standardized
	time series. For these estimators, we establish (i) their limiting
	distributions as the sample size increases while the ratio of the
	sample size to the batch size remains fixed; and (ii) their mean-square
	convergence to the variance parameter as both the batch size and
	the ratio of the sample size to the batch size increase. Compared
	with their counterparts computed from nonoverlapping batches, the
	estimators computed from overlapping batches asymptotically achieve
	reduced variance while maintaining the same bias as the sample size
	increases; moreover, the new variance estimators usually achieve
	similar improvements compared with the conventional variance estimators
	based on nonoverlapping or overlapping batch means. In follow-up
	work, we present several analytical and Monte Carlo examples, and
	we formulate efficient procedures for computing the overlapping estimators
	with only order-of-sample-size effort.}
}

@INCOLLECTION{attouch_wets_81,
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}

@INCOLLECTION{bayraksan_morton_09,
  author = {G. Bayraksan and D.P. Morton},
  title = {Assessing Solution Quality in Stochastic Programs via Sampling},
  booktitle = {Tutorials in Operations Research},
  publisher = {INFORMS},
  year = {2009},
  volume = {5},
  pages = {102--122},
  address = {Hanover, MD}
}

@ARTICLE{Bayraksan2006,
  author = {Bayraksan,, G. and Morton,, D. P.},
  title = {Assessing solution quality in stochastic programs},
  journal = {Mathematical Programming},
  year = {2006},
  volume = {108},
  pages = {495--514},
  number = {2}
}

@ARTICLE{bertocchi_etal_99,
  author = {M. Bertocchi and J. Dupa{\v{c}}ov{\'{a}} and V. Moriggia},
  title = {Sensitivity of Bond Portfolio's Behavior with Respect to Random Movements
	in Yield Curve: A Simulation Study},
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  pages = {267-286}
}

@ARTICLE{damerdji1995mean,
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	simulation output analysis},
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  number = {2},
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}

@ARTICLE{damerdji1994strong,
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  title = {{Strong consistency of the variance estimator in steady-state simulation
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@ARTICLE{dupacova_wets_88,
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@BOOK{higle1996,
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@ARTICLE{hu2010sample,
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	programs},
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}

@ARTICLE{janjarassuk_linderoth_08,
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@ARTICLE{king_rockafellar_93,
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@ARTICLE{kleywegt2002sample,
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@BOOK{law_07,
  title = {Simulation Modeling and Analysis},
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  year = {2007},
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  edition = {4}
}

@INPROCEEDINGS{love2011overlapping,
  author = {Love, D. and Bayraksan, G.},
  title = {Overlapping Batches for the Assessment of Solution Quality in Stochastic
	Programs},
  booktitle = {Proceedings of the 2011 Winter Simulation Conference},
  year = {2011},
  editor = {S. Jain and R.R. Creasey and J. Himmelspach and K.P. White and M.
	Fu},
  pages = {4184--4195},
  address = {Piscataway, New Jersey},
  month = dec,
  publisher = {Institute of Electrical and Electronics Engineers, Inc.}
}

@ARTICLE{Mak1999,
  author = {W. Mak and D. P. Morton and R. K. Wood},
  title = {Monte {C}arlo bounding techniques for determining solution quality
	in stochastic programs},
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  number = {1-2}
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@ARTICLE{matsumoto_nishimura_98,
	AUTHOR={M. Matsumoto and T. Nishimura},
	TITLE={Mersenne Twister: A 623--Dimensionally Equidistributed Uniform Pseudo-Random Number Generator},
	JOURNAL={{ACM} Transactions on Modeling and Computer Simulation},
	VOLUME={8},
	NUMBER={1},
	YEAR={1998},
	PAGES={3-30}
}

@INPROCEEDINGS{Meketon1984,
  author = {Meketon, M.S. and Schmeiser, B.},
  title = {{Overlapping batch means: Something for nothing?}},
  booktitle = {Proceedings of the 1984 Winter Simulation Conference},
  year = {1984},
  editor = {S. Sheppard and U. Pooch and D. Pegden},
  pages = {227--230},
  address = {Piscataway, New Jersey},
  month = dec,
  publisher = {Institute of Electrical and Electronics Engineers, Inc.}
}

@ARTICLE{Meterelliyoz_etal_12,
  author = {Melike Meterelliyoz and Christos Alexopoulos and David Goldsman},
  title = {Folded overlapping variance estimators for simulation },
  journal = {European Journal of Operational Research },
  year = {2012},
  volume = {220},
  pages = {135 - 146},
  number = {1}
}

@ARTICLE{norkin_pflug_ruszczynski_98,
  author = {V.I. Norkin and G.Ch. Pflug and A. Ruszczy{\'{n}}ski},
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  journal = {Mathematical Programming},
  year = {1998},
  volume = {83},
  pages = {425-450}
}

@BOOK{partani_07,
  title = {Adaptive Jacknife Estimators for Stochastic Programming},
  publisher = {Ph.D. dissertation, The University of Texas, Austin, Texas},
  year = {2007},
  author = {A. Partani}
}

@INPROCEEDINGS{partani2006jackknife,
  author = {A. Partani and D.P. Morton and I. Popova},
  title = {Jackknife estimators for reducing bias in asset allocation},
  booktitle = {Proceedings of the 2006 Winter Simulation Conference},
  year = {2006},
  editor = {L. F. Perrone and F. P. Wieland and J. Liu and B. G. Lawson and D.
	M. Nicol and R. M. Fujimoto},
  pages = {783--791},
  address = {Piscataway, New Jersey},
  month = dec,
  publisher = {Institute of Electrical and Electronics Engineers, Inc.}
}

@BOOK{Resnick1999,
  title = {A Probability Path},
  publisher = {Birkh{\"a}user Boston},
  year = {1999},
  author = {Resnick, S.},
  month = oct
}

@ARTICLE{ruszczynski1986regularized,
  author = {Ruszczy{\'n}ski, A.},
  title = {{A regularized decomposition method for minimizing a sum of polyhedral
	functions}},
  journal = {Mathematical Programming},
  year = {1986},
  volume = {35},
  pages = {309--333},
  number = {3},
  publisher = {Springer}
}

@ARTICLE{ruszczynski1997accelerating,
  author = {Ruszczy{\'n}ski, A. and Swietanowski, A.},
  title = {{Accelerating the regularized decomposition method for two stage
	stochastic linear problems}},
  journal = {European Journal of Operational Research},
  year = {1997},
  volume = {101},
  pages = {328--342},
  number = {2},
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}

@ARTICLE{santoso_ahmed_etal_05,
  author = {T. Santoso and S. Ahmed and M. Goetschalckx and A. Shapiro},
  title = {A Stochastic Programming Approach for Supply Chain Network Design
	under Uncertainty},
  journal = {European Journal of Operational Research},
  year = {2005},
  volume = {167},
  pages = {96-115}
}

@CONFERENCE{SAH90,
  author = {B. Schmeiser and T. N. Avramidis and S. Hashem},
  title = {Overlapping Batch Statistics},
  booktitle = {Proceedings of the 1990 Winter Simulation Conference},
  year = {1990},
  editor = {Balci, O. and Sadowski, R. P. and Nance, R. E.},
  pages = {395--398},
  address = {Piscataway, New Jersey},
  month = dec,
  publisher = {Institute of Electrical and Electronics Engineers, Inc.}
}

@INCOLLECTION{shapiro_03,
  author = {A.~Shapiro},
  title = {{M}onte {C}arlo sampling methods},
  booktitle = {Handbooks in Operations Research and Management Science, Volume 10:
	Stochastic Programming},
  publisher = {Elsevier},
  year = {2003},
  editor = {A. Ruszczy{\'{n}}ski and A. Shapiro},
  pages = {353-425}
}

@ARTICLE{shapiro_91,
  author = {A. Shapiro},
  title = {Asymptotic analysis of stochastic programs},
  journal = {Annals of Operations Research},
  year = {1991},
  volume = {30},
  pages = {169-186}
}

@ARTICLE{shapiro2000rate,
  author = {Shapiro, A. and Homem-de-Mello, T.},
  title = {On the rate of convergence of optimal solutions of {M}onte {C}arlo
	approximations of stochastic programs},
  journal = {SIAM Journal on Optimization},
  year = {2000},
  volume = {11},
  pages = {70--86},
  number = {1},
  publisher = {Society for Industrial and Applied Mathematics}
}

@ARTICLE{Song1992,
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}

@MISC{wagner_twister_09,
  author = {R.J. Wagner and R. Berg},
  title = {Mersenne {T}wister Random Number Generator},
  howpublished = {\url{http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/VERSIONS/C-LANG/MersenneTwister.h}
	[Last accessed 16-October-2013]},
  year = {2013}
}

@ARTICLE{wang_ahmed_08,
  author = {W. Wang and S. Ahmed},
  title = {Sample average approximation of expected value constrained stochastic
	programs},
  journal = {Operations Research Letters},
  year = {2008},
  volume = {36},
  pages = {515-519}
}

@INPROCEEDINGS{Welch1987,
  author = {Welch, P. D.},
  title = {On the relationship between batch means, overlapping means and spectral
	estimation},
  booktitle = {Proceedings of the 1987 Winter Simulation Conference},
  year = {1987},
  editor = {Thesen, A. and Grant, H. and Kelton, W. D.},
  pages = {320--323},
  address = {Piscataway, New Jersey},
  month = dec,
  publisher = {Institute of Electrical and Electronics Engineers, Inc.}
}