CORRELATION-ANALYSIS OF EXTREME OBSERVATIONS FROM A MULTIVARIATE NORMAL-DISTRIBUTION

In measuring visual acuity, the extremes of a set of normally distribu ted measures are of concern, together with one or more covariates. Thi s leads to a model in which (X, Y-1, Y-2) are jointly normally distrib uted with Y-1, Y-2 exchangeable and (X, Y-i) having a common correlati on. Inferential procedures are developed for correlations and linear r egressions among X and the ordered Y values. This requires determinati on of the covariance matrix of X, Y-(1) = min{Y-1, Y-2} and Y(2) = max (Y-1, Y-2). The inadequacy of certain estimates that ignore the nonnor mality of {X, Y-(1), Y-(2)} is also discussed. Although the bivariate case is emphasized because of the context of the visual acuity model, many results are given for the more general multivarjate case.