{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T05:18:30Z","timestamp":1672291110272},"reference-count":8,"publisher":"Association for Computing Machinery (ACM)","issue":"4","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Model. Comput. Simul."],"published-print":{"date-parts":[[2006,10]]},"abstract":"Independent replications (IR) and batch means (BM) are two of the most widely used variance-estimation methods for simulation output analysis. Alexopoulos and Goldsman conducted a thorough examination of IR and BM; and Andrad\u00f3ttir and Argon proposed the method of replicated batch means (RBM), which combines good characteristics of IR and BM. This article gives analy-tical results for the mean and variance of the RBM estimator for a class of processes having initial transients with an additive form. Along the way, we provide succinct complementary extensions of some of the results in the aforementioned papers. Our expressions explicitly show how the transient function affects estimator performance and suggest that in some cases, the RBM estimator is a good compromise choice with respect to bias and variance. However, care must be taken to avoid an excessive number of replications when the transient function is pervasive. An example involving a simple moving average process illustrates our findings.<\/jats:p>","DOI":"10.1145\/1176249.1176250","type":"journal-article","created":{"date-parts":[[2007,1,16]],"date-time":"2007-01-16T19:38:29Z","timestamp":1168976309000},"page":"317-328","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Replicated batch means variance estimators in the presence of an initial transient"],"prefix":"10.1145","volume":"16","author":[{"given":"Christos","family":"Alexopoulos","sequence":"first","affiliation":[{"name":"Georgia Institute of Technology, Atlanta, GA"}]},{"given":"Sigr\u00fan","family":"Andrad\u00f3ttir","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, Atlanta, GA"}]},{"given":"Nilay Tanik","family":"Argon","sequence":"additional","affiliation":[{"name":"University of North Carolina at Chapel Hill, NC"}]},{"given":"David","family":"Goldsman","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, Atlanta, GA"}]}],"member":"320","published-online":{"date-parts":[[2006,10]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/974734.974738"},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1002\/nav.20158","article-title":"Replicated batch means for steady-state simulations","volume":"53","author":"Argon N. T.","year":"2006","unstructured":"Argon , N. T. and Andrad\u00f3ttir , S. 2006 . Replicated batch means for steady-state simulations . Naval Res. Log. 53 , 6, 508 -- 524 . Argon, N. T. and Andrad\u00f3ttir, S. 2006. Replicated batch means for steady-state simulations. Naval Res. Log. 53, 6, 508--524.","journal-title":"Naval Res. Log."},{"key":"e_1_2_1_3_1","volume-title":"Convergence of Probability Measures","author":"Billingsley P.","unstructured":"Billingsley , P. 1968. Convergence of Probability Measures . Wiley , New York . Billingsley, P. 1968. Convergence of Probability Measures. Wiley, New York."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.43.9.1288"},{"key":"e_1_2_1_6_1","volume-title":"Discrete-Event Simulation: Modeling, Programming, and Analysis","author":"Fishman G. S.","unstructured":"Fishman , G. S. 2001. Discrete-Event Simulation: Modeling, Programming, and Analysis . Springer-Verlag , New York . Fishman, G. S. 2001. Discrete-Event Simulation: Modeling, Programming, and Analysis. Springer-Verlag, New York."},{"key":"e_1_2_1_7_1","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1080\/07408179008964153","article-title":"The correlation between mean and variance estimators in computer simulation","volume":"22","author":"Kang K.","year":"1990","unstructured":"Kang , K. and Goldsman , D. 1990 . The correlation between mean and variance estimators in computer simulation . IIE Trans. 22 , 15 -- 23 . Kang, K. and Goldsman, D. 1990. The correlation between mean and variance estimators in computer simulation. IIE Trans. 22, 15--23.","journal-title":"IIE Trans."},{"key":"e_1_2_1_8_1","unstructured":"Patel J. K. and Read C. B. 1996. Handbook of the Normal Distribution 2nd ed. Marcel Dekker New York. Patel J. K. and Read C. B. 1996. Handbook of the Normal Distribution 2nd ed. Marcel Dekker New York."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.41.1.110"}],"container-title":["ACM Transactions on Modeling and Computer Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1176249.1176250","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T20:09:28Z","timestamp":1672258168000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1176249.1176250"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,10]]}},"alternative-id":["10.1145\/1176249.1176250"],"URL":"http:\/\/dx.doi.org\/10.1145\/1176249.1176250","relation":{},"ISSN":["1049-3301","1558-1195"],"issn-type":[{"value":"1049-3301","type":"print"},{"value":"1558-1195","type":"electronic"}],"subject":["Computer Science Applications","Modeling and Simulation"],"published":{"date-parts":[[2006,10]]},"assertion":[{"value":"2006-10-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}