Bileşen yaklaşımıyla çok boyutlu durum için umbrella test

Abstract

Bu çalışmada, Gregory A.Mack ve Dougles A. Wolfe [Bkz 5] tarafından tek boyutlu durum için geliştirilmiş olan Umbrella testini çok boyutlu durum için bileşen yaklaşımıyla genelledik. Öncelikle çok boyutlu durum için bir Ag test istatistiği oluşturuldu. ZU«* + I V m g=l,'...p \In this study, Umbrella Test for univariate case developed by Gregory A. Mack and Douglas A. Wolfe has been generalized to multivariate case with component -wise approach. Firstly, an Ag test statistics for multivariate case has been constructed. Secondly, it is shown that under null hypothesis the asymptotic distribution is p variate normal with the expected value 0 and the covariance matrix is 2, = '-£ *'. 7=1 J=t k r. - ı k i = i j = e + i P gh /36 Moreover, to be able to get the relative efficiency values, the asymptotic asymptotic distribution of Ag test statistics had been developed under the local alternative. Furthermore, the univariate Umbrella test developed by using the normal theory approach has been generalized for the multivariate case. Finally, a critical values for a finite sample size under predetermined oc values has been calculated.