Kaizhao Liu, Jose Blanchet, Lexing Ying, Yiping Lu
arXiv 29 Apr 2024 · Statistics — Methodology
arXiv:2404.19145 · PDF · DOI · OpenAlex · Extracted main text
Bootstrap is a popular methodology for simulating input uncertainty. However, it can be computationally expensive when the number of samples is large. We propose a new approach called Orthogonal Bootstrap that reduces the number of required Monte Carlo replications. We decomposes the target being simulated into two parts: the non-orthogonal part which has a closed-form result known as Infinitesimal Jackknife and the orthogonal part which is easier to be simulated. We theoretically and numerically show that Orthogonal Bootstrap significantly reduces the computational cost of Bootstrap while improving empirical accuracy and maintaining the same width of the constructed interval.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Lam, H (2022) A cheap bootstrap method for fast inference | 1.000 | 16 | 3 | 100% |
| 2 | Efron, B (1992) Bootstrap methods: another look at the jackknife | 1.000 | 6 | 3 | 100% |
| 3 | Cook, R. D. and Weisberg, S (1980) Characterizations of an empirical influence function for detecting influential cases in regression | 1.000 | 5 | 3 | 100% |
| 4 | Ma, C. and Ying, L (2022) Correcting convexity bias in function and functional estimate self | 0.965 | 10 | 4 | 90% |
| 5 | Koh, P. W. and Liang, P (2017) Understanding black-box predictions via influence functions | 0.941 | 6 | 4 | 83% |
| 6 | Efron, B (1982) The jackknife, the bootstrap and other resampling plans | 0.811 | 4 | 2 | 100% |
| 7 | Etter, P. A. and Ying, L (2020) Operator augmentation for noisy elliptic systems self | 0.811 | 4 | 2 | 100% |
| 8 | Etter, P. and Ying, L (2021) Operator augmentation for general noisy matrix systems self | 0.811 | 4 | 2 | 100% |
| 9 | Jiao, J. and Han, Y (2020) Bias correction with jackknife, bootstrap, and taylor series | 0.811 | 4 | 2 | 100% |
| 10 | Koltchinskii, V. and Zhilova, M (2021) Estimation of smooth functionals in normal models: bias reduction and asymptotic efficiency | 0.811 | 4 | 2 | 100% |
Showing the top 10 of 65 scored citations.