{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T11:47:38Z","timestamp":1763466458347,"version":"3.32.0"},"reference-count":31,"publisher":"Association for Computing Machinery (ACM)","issue":"1","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Model. Comput. Simul."],"published-print":{"date-parts":[[2007,1]]},"abstract":"<jats:p>The time-average estimator is typically biased in the context of steady-state simulation, and its bias is of order 1\/<jats:italic>t<\/jats:italic>, where<jats:italic>t<\/jats:italic>represents simulated time. Several \u201clow-bias\u201d estimators have been developed that have a lower order bias, and, to first-order, the same variance of the time-average. We argue that this kind of first-order comparison is insufficient, and that a second-order asymptotic expansion of the mean square error (MSE) of the estimators is needed. We provide such an expansion for the time-average estimator in both the Markov and regenerative settings. Additionally, we provide a full bias expansion and a second-order MSE expansion for the Meketon--Heidelberger low-bias estimator, and show that its MSE can be asymptotically higher or lower than that of the time-average depending on the problem. The situation is different in the context of parallel steady-state simulation, where a reduction in bias that leaves the first-order variance unaffected is arguably an improvement in performance.<\/jats:p>","DOI":"10.1145\/1189756.1189760","type":"journal-article","created":{"date-parts":[[2007,1,16]],"date-time":"2007-01-16T19:38:29Z","timestamp":1168976309000},"page":"4","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["On the theoretical comparison of low-bias steady-state estimators"],"prefix":"10.1145","volume":"17","author":[{"given":"Hernan P.","family":"Awad","sequence":"first","affiliation":[{"name":"University of Miami, Coral Gables, FL"}]},{"given":"Peter W.","family":"Glynn","sequence":"additional","affiliation":[{"name":"Stanford University, Stanford, CA"}]}],"member":"320","published-online":{"date-parts":[[2007,1]]},"reference":[{"key":"e_1_2_1_1_1","first-page":"27","article-title":"Some use of computers in operational research","volume":"31","author":"Beale E. 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