Skewness of a randomized quasi-Monte Carlo estimate
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908281831686144 |
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| author | Pan, Zexin Owen, Art B. |
| author_facet | Pan, Zexin Owen, Art B. |
| contents | Some recent work on confidence intervals for randomized quasi-Monte Carlo (RQMC) sampling found a surprising result: ordinary Student $t$ 95% confidence intervals based on a modest number of replicates were seen to be very effective and even more reliable than some bootstrap $t$ intervals that were expected to be best. One potential explanation is that those RQMC estimates have small skewness. In this paper we give conditions under which the skewness is $O(n^ε)$ for any $ε>0$, so 'almost $O(1)$'. Under a random generator matrix model, we can improve this rate to $O(n^{-1/2+ε})$ with very high probability. We also improve some probabilistic bounds on the distribution of the quality parameter $t$ for a digital net in a prime base under random sampling of generator matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06136 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Skewness of a randomized quasi-Monte Carlo estimate Pan, Zexin Owen, Art B. Numerical Analysis Computation Some recent work on confidence intervals for randomized quasi-Monte Carlo (RQMC) sampling found a surprising result: ordinary Student $t$ 95% confidence intervals based on a modest number of replicates were seen to be very effective and even more reliable than some bootstrap $t$ intervals that were expected to be best. One potential explanation is that those RQMC estimates have small skewness. In this paper we give conditions under which the skewness is $O(n^ε)$ for any $ε>0$, so 'almost $O(1)$'. Under a random generator matrix model, we can improve this rate to $O(n^{-1/2+ε})$ with very high probability. We also improve some probabilistic bounds on the distribution of the quality parameter $t$ for a digital net in a prime base under random sampling of generator matrices. |
| title | Skewness of a randomized quasi-Monte Carlo estimate |
| topic | Numerical Analysis Computation |
| url | https://arxiv.org/abs/2405.06136 |