Let {Xj}j=1n1 and {Yk}k=1n2 be independent samples from F1 and F2 respectively. {Xj} and {Yk} are assumed to be mutually independent. Let φ(x1, …, xm1;y1, …, ym2) be Borel measurable function which is symmetric in ...
Let {Xm} be a sequence of i. i. d. random variables with common distribution function F(x). Define U-statistic by where φ is a symmetric function of two variables with Eφ(X1, X2)=0. Our results generalize the Be...