$U$-Statistic Processes: A Martingale Approach

Abstract

E/-STATISTIC PROCESSES 1729 Since (assuming no ties) /U pV I h(x,y)l{xfiy}Fn(dx)Fn(dy), -oo J—oo we may write the equation in Corollary 1.1 as n fu Г ——- / / h(x,y)l{x/y}Fn(dx)Fn(dy) =Un(u,v) n *■ J—oo J—oo = ffh(x,y)Fn(dx)F(dy) J—oo J—oo + Г Г h(x,y)F(dx)Fn(dy) ...