TY - GEN
T1 - Sufficient Conditions for a Central Limit Theorem to Assess the Error of Randomized Quasi-Monte Carlo Methods
AU - Nakayama, Marvin K.
AU - Tuffin, Bruno
N1 - Funding Information:
MARVIN K. NAKAYAMA is a professor in the Department of Computer Science at the New Jersey Institute of Technology. He received an M.S. and Ph.D. in operations research from Stanford University and a B.A. in mathematics-computer science from U.C. San Diego. He is a recipient of a CAREER Award from the National Science Foundation, and a paper he co-authored received the Best Theoretical Paper Award for the 2014 Winter Simulation Conference. He is an associate editor for ACM Transactions on Modeling and Computer Simulation, and served as the simulation area editor for the INFORMS Journal on Computing from 2007–2016. His research interests include simulation, modeling, statistics, risk analysis, and energy. His email address is marvin@njit.edu.
Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - Randomized quasi-Monte Carlo (RQMC) can produce an estimator of a mean (i.e., integral) with root-mean-square error that shrinks at a faster rate than (standard) Monte Carlo's. While RQMC is commonly employed to provide a confidence interval (CI) for the mean, this approach implicitly assumes that the RQMC estimator obeys a central limit theorem (CLT), which has not been established for most RQMC settings. To address this, we provide various conditions that ensure an RQMC CLT, as well as an asymptotically valid CI, and examine the tradeoffs in our restrictions. Our sufficient conditions, depending on the regularity of the integrand, often require that the number of randomizations grows sufficiently fast relative to the number of points used from the low-discrepancy sequence.
AB - Randomized quasi-Monte Carlo (RQMC) can produce an estimator of a mean (i.e., integral) with root-mean-square error that shrinks at a faster rate than (standard) Monte Carlo's. While RQMC is commonly employed to provide a confidence interval (CI) for the mean, this approach implicitly assumes that the RQMC estimator obeys a central limit theorem (CLT), which has not been established for most RQMC settings. To address this, we provide various conditions that ensure an RQMC CLT, as well as an asymptotically valid CI, and examine the tradeoffs in our restrictions. Our sufficient conditions, depending on the regularity of the integrand, often require that the number of randomizations grows sufficiently fast relative to the number of points used from the low-discrepancy sequence.
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U2 - 10.1109/WSC52266.2021.9715427
DO - 10.1109/WSC52266.2021.9715427
M3 - Conference contribution
AN - SCOPUS:85126101497
T3 - Proceedings - Winter Simulation Conference
BT - 2021 Winter Simulation Conference, WSC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2021 Winter Simulation Conference, WSC 2021
Y2 - 12 December 2021 through 15 December 2021
ER -