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Infinite-order U-statistics (IOUS) has been used extensively on subbagging ensemble learning algorithms such as random forests to quantify its uncertainty.
[author] Hoeffding, WassilyW. (1948). A Class of Statistics with Asymptotically Normal Distribution. Ann. Math. Statist. 19 293–325. 10.1214/aoms/1177730196
1948
Earlier work this paper cites.
[author] Horvitz, Daniel GD. G. and Thompson, Donovan JD. J. (1952). A Generalization of Sampling Without Replacement From a Finite Universe. Journal of the American Statistical Association 47 663–685
1952
Earlier work this paper cites.
[author] Sen, Amode RA. R. (1953). On the Estimate of the Variance in Sampling With Varying Probabilities. Journal of the Indian Society of Agricultural Statistics 5 127
1953
Earlier work this paper cites.
[author] Yates, FrankF. and Grundy, P MichaelP. M. (1953). Selection Without Replacement from Within Strata with Probability Proportional to Size. Journal of the Royal Statistical Society: Series B (Methodological) 15 253–261
1953
Earlier work this paper cites.
[author] Sen, Pranab KumarP. K. (1960). On some convergence properties of U-statistics. Calcutta Statistical Association Bulletin 10 1–18
1960
Earlier work this paper cites.
[author] Efron, BradleyB. and Stein, CharlesC. (1981). The Jackknife Estimate of Variance. The Annals of Statistics 586–596
1981
Earlier work this paper cites.
[author] Folsom, Ralph ER. E. (1984). Probability Sample U-statistics: Theory and Applications for Complex Sample Designs, PhD thesis, The University of North Carolina at Chapel Hill
1984
Earlier work this paper cites.
[author] Frees, Edward WE. W. (1989). Infinite Order U-statistics. Scandinavian Journal of Statistics 29–45
1989
Earlier work this paper cites.
[author] Schucany, William RW. R. and Bankson, Daniel MD. M. (1989). Small sample variance Estimators for U-statistics. Australian Journal of Statistics 31 417–426
1989
Earlier work this paper cites.
[author] Lee, A JA. J. (1990). U-statistics: Theory and Practice. CRC Press
1990
Earlier work this paper cites.
[author] Friedman, Jerome HJ. H. (1991). Multivariate Adaptive Regression Splines. The Annals of Statistics 1–67
1991
Cited alongside, same era.
[author] Breiman, LeoL. (2001). Random Forests. Machine Learning 45 5–32
2001
Cited alongside, same era.
[author] Geurts, PierreP., Ernst, DamienD. and Wehenkel, LouisL. (2006). Extremely Randomized Trees. Machine Learning 63 3–42
2006
Cited alongside, same era.
[author] Cochran, William GW. G. (2007). Sampling Techniques, 3 ed. John Wiley & Sons
2007
Cited alongside, same era.
[author] Biau, GérardG. (2012). Analysis of a Random Forests Model. The Journal of Machine Learning Research 13 1063–1095
2012
Cited alongside, same era.
[author] Wager, StefanS. and Athey, SusanS. (2018). Estimation and Inference of Heterogeneous Treatment Effects using Random Forests. Journal of the American Statistical Association 113 1228-1242. 10.1080/01621459.2017.1319839
2017
Later among the works it cites.
[author] Wang, QingQ. and Lindsay, BruceB. (2017). Pseudo-kernel method in U-statistic variance estimation with large kernel size. Statistica Sinica 1155–1174
2017
Later among the works it cites.
[author] Athey, SusanS., Tibshirani, JulieJ. and Wager, StefanS. (2019). Generalized Random Forests. The Annals of Statistics 47 1148–1178
2019
Later among the works it cites.
[author] Chen, XiaohuiX. and Kato, KengoK. (2019). Randomized incomplete U U -statistics in high dimensions. The Annals of Statistics 47 3127–3156
2019
Later among the works it cites.
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2012
Cited alongside, same era.
[author] Efron, BradleyB. (2014). Estimation and Accuracy After Model Selection. Journal of the American Statistical Association 109 991–1007
2014
Cited alongside, same era.
[author] Wager, StefanS., Hastie, TrevorT. and Efron, BradleyB. (2014). Confidence intervals for random forests: The jackknife and the infinitesimal jackknife. The Journal of Machine Learning Research 15 1625–1651
2014
Cited alongside, same era.
[author] Wang, QingQ. and Lindsay, BruceB. (2014). Variance Estimation of a General U-statistic with Application to Cross-validation. Statistica Sinica 1117–1141
2014
Cited alongside, same era.
[author] Mentch, LucasL. and Hooker, GilesG. (2016). Quantifying Uncertainty in Random Forests via Confidence Intervals and Hypothesis Tests. Journal of Machine Learning Research 17 841–881
2016
Cited alongside, same era.
[author] Song, YangleiY., Chen, XiaohuiX. and Kato, KengoK. (2019). Approximating high-dimensional infinite-order U U -statistics: Statistical and computational guarantees. Electronic Journal of Statistics 13 4794–4848
2019
Later among the works it cites.
2021
Later among the works it cites.
[author] Zhou, ZhengzeZ., Mentch, LucasL. and Hooker, GilesG. (2021). V-statistics and Variance Estimation. Journal of Machine Learning Research 22 1–48
2021
Later among the works it cites.
[author] DiCiccio, CyrusC. and Romano, JosephJ. (2022). CLT for U-Statistics with Growing Dimension. Statistica Sinica 32 1–22
2022
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[author] Peng, WeiW., Coleman, TimT. and Mentch, LucasL. (2022). Rates of convergence for random forests via generalized U-statistics. Electronic Journal of Statistics 16 232–292
2022
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[author] Wang, QingQ. and Wei, YujieY. (2022). Quantifying uncertainty of subsampling-based ensemble methods under a U-statistic framework. Journal of Statistical Computation and Simulation 1–21
2022
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