Skewness of a randomized quasi-Monte Carlo estimate
<|reference_start|>Skewness of a randomized quasi-Monte Carlo estimate: 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 $O(n^\epsilon)$ for any $\epsilon>0$, so `almost $O(1)$'. Under a random generator matrix model, we can improve this rate to $O(n^{-1/2+\epsilon})$ 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.<|reference_end|>
@article{pan2024skewness,
    title={Skewness of a randomized quasi-Monte Carlo estimate},
    author={Zexin Pan and Art B. Owen},
    journal={arXiv preprint arXiv:2405.06136},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.06136},
    primaryClass={math.NA cs.NA stat.CO}
}