@article{5219cee82e154d33b8e79e56b886895d,
title = "Variance and derivative estimation of virtual performance",
abstract = "Virtual performance is a class of time-dependent performance measures conditional on a particular event occurring at time τ0 for a (possibly) nonstationary stochastic process; virtual waiting time of a customer arriving to a queue at time τ0 is one example. Virtual statistics are estimators of the virtual performance. In this article, we go beyond the mean to propose estimators for the variance, and for the derivative of the mean with respect to time, of virtual performance, examining both their small-sample and asymptotic properties. We also provide a modified K-fold cross validation method for tuning the parameter k for the differencebased variance estimator, and we evaluate the performance of both variance and derivative estimators via controlled studies and a realistic illustration. The variance and derivative provide useful information that is not apparent in the mean of virtual performance.",
keywords = "Nearest-neighbor regression, Output analysis, Queueing simulation",
author = "Yujing Lin and Nelson, {Barry L.}",
note = "Funding Information: This research was partially supported by the National Science Foundation under Grant No. CMMI-1537060 and GOALI co-sponsor SAS Institute. A less complete version of this work previously appeared in Lin and Nelson (2017). Authors{\textquoteright} addresses: Y. Lin, Amazon.com, 1743 NW 63rd Street, Unit A, Seattle, WA, 98107; email: yjlin17@gmail.com; B. L. Nelson, Department of Industrial Engineering & Management Sciences, Northwestern University, Evanston, IL 60208-3119 USA; email: nelsonb@northwestern.edu. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. {\textcopyright} 2018 ACM 1049-3301/2018/07-ART17 $15.00 https://doi.org/10.1145/3209959 Publisher Copyright: {\textcopyright} 2018 ACM.",
year = "2018",
month = aug,
doi = "10.1145/3209959",
language = "English (US)",
volume = "28",
journal = "ACM Transactions on Modeling and Computer Simulation",
issn = "1049-3301",
publisher = "Association for Computing Machinery (ACM)",
number = "3",
}