Asymptotic Normality of Anti-symmetric K-U Statistic

In this paper,is called the anti-symmetric K-U statistic, whereh(x,y) = - h(y,x) is an anti-symmetric function. Whenk is constant and k = O(nδ) where 0δ1/2, the asymptotic normality of the anti-symmetric K-U statistic will be established respectively.