Abstract
DeGroot, Feder, and Goel considered the problem of match-making. If (Xi, Yi), i = l, 2,…, n be a sample from a bivariate population so that Yi given Xi is normal with mean Xi and variance one. If n = (X(1), X(2),…, X(n)), n = (Y (1), Y(2),…, Y(n)) be the order statistics of the X sample and the Y sample respectively. The chapter matches the Xs with the Ys that originally were their partners, that is, it reconstructs the original sample (Xi, Yi), i = l, 2,…,n. A perfect matching would be (X(1) , YD1), (X(2), YD2), …, (X(n) , YDn) where the Ds are the antiranks of the Xs, that is, X(i) = XD.
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