F-tests for Hypotheses with Block Matrices and Under Conditions of Orthogonality in the General Multivariate Gauss-Markoff Model
✍ Scribed by Prof. dr Wiktor Oktaba
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 233 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0323-3847
No coin nor oath required. For personal study only.
✦ Synopsis
The multivariate general Gauss-Markoff (MGM) model ( U , X B , z 8 0 2 V ) when the matrices V&O and x = -O are known and the scalsr u2 >O is unknown, is considered. The present paper is a continuation of two earlier works (OKTABA, 1988a, b). If X B = X l r ; X z A , then the F-test for verificstion the hypothesis WI'A =O la presented. Moreover, under conditions of orthogonality the decomposition of the matrix S A = ( L k A ) ' L -( L h ) into the sum of s=r(L) matrices is given, where LBA is the estimator of the parametric estimable functions LBA, ) is the linear space generated by the colums of A. Then under additional assumption on normality of U the statistics F for testing LBA =O is deduced.
Under conditions of normality of U and decomposition of S A , the statistics Fl, . . ., Fs for the hypotheses Z,'BA=O ( i = l , . . i, 8) are established.