Sufficient Conditions for a Central Limit Theorem to Assess the Error of Randomized Quasi-Monte Carlo Methods
Document Type
Conference Proceeding
Publication Date
1-1-2021
Abstract
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.
Identifier
85126101497 (Scopus)
ISBN
[9781665433112]
Publication Title
Proceedings Winter Simulation Conference
External Full Text Location
https://doi.org/10.1109/WSC52266.2021.9715427
ISSN
08917736
Volume
2021-December
Fund Ref
National Science Foundation
Recommended Citation
Nakayama, Marvin K. and Tuffin, Bruno, "Sufficient Conditions for a Central Limit Theorem to Assess the Error of Randomized Quasi-Monte Carlo Methods" (2021). Faculty Publications. 4689.
https://digitalcommons.njit.edu/fac_pubs/4689