Asymptotic properties of linear combinations of U-statistics with degenerate kernels
Hajime Yamato, Masao Kondo, Koichiro Toda · Journal of nonparametric statistics · 2005
As an estimator of a real estimable parameter, we consider a linear combination of U-statistics which include V-statistic and limit of Bayes estimate [Toda, K. and Yamato, H. (2001). Berry-Esseen bounds for some statistics including LB-statistic and V-statistic. J. Japan Statis. Soc., 31, 225–237.]. In the case that the kernel of the estimable parameter is degenerated, we show functional limit theorems (invariance principles) for the linear combination of U-statistics. As their applications we give the asymptotic distribution of a linear combination of U-statistics.