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

Let U n be U -statistics based on a symmetric kernel h ( x , y ) and i.i.d. samples { X n ; n ≥ 1 } . In this paper, under some suitable conditions, we show that a general law for the moment convergence of U -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.