Multivariate generalizations . In multivariate statistical analysis, common terms such as variances and correlation coefficients have received certain generalizations. Wilks (7) has called the determinant | V |, where V is the matrix of variances and covariances between several variates, a generalized variance; certain ratios of such determinants have been called by Hotelling(5) vector correlation coefficients and vector alienation coefficients. While these determinantal functions have properties which justify to some extent this kind of generalization, it sometimes seems more reasonable to leave any generalized parameters, or corresponding sample statistics, in the form of matrices of elementary quantities. This is stressed by the formal analogy which then often exists between the generalized and the elementary formulae.
[1]
S. S. Wilks.
CERTAIN GENERALIZATIONS IN THE ANALYSIS OF VARIANCE
,
1932
.
[2]
M. S. Bartlett,et al.
The vector representation of a sample
,
1934,
Mathematical Proceedings of the Cambridge Philosophical Society.
[3]
A. C. Aitken,et al.
Note on Selection from a Multivariate Normal Population
,
1935
.
[4]
H. Hotelling.
Relations Between Two Sets of Variates
,
1936
.
[5]
D. Lawley.
A GENERALIZATION OF FISHER'S z TEST
,
1938
.
[6]
R. Fisher.
THE STATISTICAL UTILIZATION OF MULTIPLE MEASUREMENTS
,
1938
.
[7]
M. Bartlett.
Further aspects of the theory of multiple regression
,
1938,
Mathematical Proceedings of the Cambridge Philosophical Society.