[1] Babbel B. Invariance priciples for U-statistics and Von-Mises functions. J Statisi Plann Infer, 1989, 22: 337–354

[2] Berk R H. Limiting behavior of posterior distributions when the model is incorrect. Ann Math Statist, 1966, 37: 51–58

[3] Denker M, Keller G. On U-statistics and Von-Mises’ statistics for weakly dependent processes. Z Wahrsch
Verw Gebiete, 1983, 64: 505–522

[4] Hoeffding W. A class of statistics with asymptotically normal distribution. Ann Math Statist, 1948, 19(3):
293–325

[5] Hoeffding W. The strong law of large numbers for U-statistics. Statistics, Univ North Carolina Mimeo
Series, 1961, 302

[6] Liu W D, Lin Z Y. Precise asymptotics for a new kind of complete moment convergence. Statist Probab
Lett, 2006, 76: 1787–1799

[7] Sen P K. On some convergence properties U-statistics. Calcutta Stat Assoc Bull, 1960, 10: 1–18

[8] Spffataru A. Precise asymptotics in Spiter’s law of large numbers. J Theoret Probab 1997, 12: 811–819

[9] Wang J F, Cai G H. Precise asymptotics in the some strong limit theorems for U-statistics. Appl Math J
Chinese Univ, 2004, 19(4): 436–444

[10] Wang Q Y. The strong law of U-statistics with φ -mixing samples. Stati Probab Lett, 1995, 23: 115–155

[11] Yan J G, Su C. Precise asymptotics of U-statistics. Acta Math Sinica, 2007, 50(3): 517–526

[12] Zhang Y. An inequality of U-statistics and its application. J Hangzhou University (Natural Science), 1995,
22(4): 352–358