Papers on U-statistics

List of papers on U-statistics by subjects

Fundamental

Wassily Hoeffding (1948). A Class of Statistics with Asymptotically Normal Distribution

Ann. Math. Statist., Volume 19, Number 3 (1948), 293-325.

Strong law

W Hoeffding (1961). The strong law of large numbers for u-statistics. North Carolina State University. Dept. of Statistics.
Tasos C. Christofides (1992). A strong law of large numbers for U-statistics. Journal of Statistical Planning and Inference. Volume 31, Issue 2, May 1992, Pages 133-145

Asymptotic Normality

Asymptotic Normality of studentized U-statistics

Bing-Yi Jing, Qiying Wang, and Lincheng Zhao (2000). The Berry-Esséen bound for Studentized statistics

Ann. Probab. Volume 28, Number 1 (2000), 511-535.

Stein’s method for nonlinear statistics: A brief survey and recent progress
Journal of Statistical Planning and Inference 168

Statistical inference

Hien D. Nguyen (2019). Concentration-based confidence intervals for U-statistics, ArXiv.

U-statistics with increasing degree

Edward W. Frees (1989). Infinite Order U-Statistics. Scandinavian Journal of Statistics

Vol. 16, No. 1 (1989), pp. 29-45.

Charles Heilig and Deborah Nolan (2001). Limit theorems for the infinite-degree U-process.

Statistica Sinica. Vol. 11, No. 1 (January 2001), pp. 289-302

Grzegorz A Rempala and Arjun Gupta (1999). Weak limits of U -statistics of infinite order.

Random Operators and Stochastic Equations 7(1):39-52

Berry-Esseen type bound

Louis H.Y. Chen and Qi-Man Shao (2007). Normal approximation for nonlinear statistics using a concentration inequality approach. Bernoulli, Volume 13, Number 2 (2007), 581-599.

Jackknife estimator of variance

James N. Arvesen (1969). Jackknifing U-Statistics. The Annals of Mathematical Statistics

Vol. 40, No. 6 (Dec., 1969), pp. 2076-2100

Incomplete U-statistics

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