Asymptotic Analysis for U-Statistics and Its Application to Von Mises Statistics

References

[1] V. Ulyanov and F.G?tze, “Uniform Approximations in the CLT for Balls in Euclidian Spaces,” 00-034, SFB 343, University of Bielefeld, 2000, p. 26.
http://www.math.uni-bielfeld.de/sfb343/preprints/pr00034.pdf.gz

[2] V. Bentkus and F. G?tze, “Optimal Bounds in Non- Gaussian Limit Theorems for U-Statistics,” The Annals of Probability, Vol. 27, No.1, 1999, pp. 454-521.
doi:10.1214/aop/1022677269

[3] S. A. Bogatyrev, F. G?tze and V. V. Ulyanov, “Non- Uniform Bounds for Short Asymptotic Expansions in the CLT for Balls in a Hilbert Space,” Journal of Multivariate Analysis, Vol. 97, 2006, pp. 2041-2056.

[4] T. A. Zubayraev, “Asymptotic Analysis for U-Statistics: Approximation Accuracy Estimation,” Publications of Junior Scientists of Faculty of Computational Mathematics and Cybernetics, Moscow State University, Vol. 7, 2010, pp. 99-108.
http://smu.cs.msu.su/conferences/sbornik7/smu-sbornik-7.pdf