Asymptotic Results forU-Functions of Concomitants of Order Statistics

摘要

Summary.LetX1:n#x2264; #x2026; #x2264;Xn:nbe the order statistics and letY1:n, #x2026; ,Yn:nbe the associated concomitants in a bivariate sample (X1,Y1), #x2026; , (Xn,Yn). We prove strong consistency and an asymptotic representation forU-statistics based on the concomitantsYi:nwith #x3B1;n + 1 #x2264;i#x2264;n#x2212; #xDF;n where 0 #x2264;#x3B1;,.