Central limit theorems for studentized -statistics

Abstract

For studentized U-statistics, Arvesen (1969) established a central limit theorem assuming that the second moment exists, and Zhao (1983) established the Berry-Esseen bound if !vml]>[./200501.files/image002.gif]endif]> if the 4.5-th moment exists. We show that the existence of if !vml]>[./200501.files/image004.gif] endif]> moment suffices for the central limit theorem and that the existence of if !vml]>[./200501.files/image006.gif] endif]> moment yields the Berry-Esseen bound if !vml]>[./200501.files/image008.gif] endif]> . if !supportEmptyParas]> endif]> if !supportEmptyParas]> endif]>