Siotani’s modified second approximation for multiple comparisons of mean vectors

Abstract

In the modified second approximation method for multiple comparisons of mean vectors that Professor Minoru Siotani (1959, 1960, 1964) originally proposed, it is crucial to consider the bivariate distribution of two correlated Hotelling’s $T^2$ statistics. We focus on an application of the differential operator developed by Kakizawa and Iwashita (2005a) and then derive asymptotic expansion of the bivariate distribution of $(T_{ab}^2,T_{cd}^2)$ as well as its marginal $T_{ab}^2$.