On the Efficiency of Certain Nonparametric Tests

Abstract

在統計上很熟悉的一個問題是如何檢定兩個母之分配是否相同。在此檢定中，一個時常被考慮的對立假設是：這兩個母體之分配中，其離勢不同而其他皆同。關於觀察值是一元的情況，已有甚多有母數或無母數檢定可用。然而觀察值是二元的情況，至今仍少有研究。在這篇論文中，導出了當母體具有二元常態時之可能性比率檢定，並研究其機率分配。也研究了當母體具有二元常態或二元均等分配時，兩種無母數檢定R及R*（Liu (1982)之論文中曾提出）與其競爭之有母數檢定之間的漸近相對效率。 A familiar problem is to test whether two samples have come from identical populations. A frequently considered alternative is that the populations differ only in dispersion. If the observations are univariate, several parametric or nonparametric tests have been proposed in the literature.However, the bivariate case-seems to have been studied far less fully. In this paper, the likelihood ratio test is derived and its distribution is studied if the underlying distributions are bivariate normal The asymptotic relative efficiencies of the nonparametric tests R and R* suggested in Liu (1982) with respect to the parametric competitors are also investigated for bivariate normal and bivariate uniform distributions.