Asymptotic properties for covariance matrices of order statistics

Abstract

The asymptotic eigenvectors and eigenvalues of V , the covariance matrix of order statistics, are examined, and are given for the case where the parent population is normal or uniform. It is shown how these might, be used in developing a model for goodness-of-fit tests. Some approximations are given for certain functions of V and m , the expected value vector for order statistics, which arise in tests for normality.