Precise asymptotics for complete moment convergence of UU-statistics of i.i.d. random variables

Let UnUn be UU-statistics based on a symmetric kernel h(x,y)h(x,y) and i.i.d. samples {Xn;n≥1}{Xn;n≥1}. In this paper, under some suitable conditions, we show that a general law for the moment convergence of UU-statistics holds. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in the study of precise asymptotics for complete moment convergence.