Correlation Analysis of Extreme Observations from a Multivariate Normal Distribution
研究了视觉敏锐度测量中，正态分布极端值与协变量的相关性，推导了有序极值的协方差矩阵，并讨论了忽略非正态性导致的估计偏差。
In measuring visual acuity, the extremes of a set of normally distributed measures are of concern, together with one or more covariates. This leads to a model in which (X, Y 1, Y 2) are jointly normally distributed with Y 1, Y 2 exchangeable and (X, Y i ) having a common correlation. Inferential procedures are developed for correlations and linear regressions among X and the ordered Y values. This requires determination 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 nonnormality 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 multivariate case.