This paper provides proof of conjectures about the expected values of the $j$th elementary symmetric function of the roots (i.e. $E(\operatorname{tr}_j A)$) of a non-central Wishart matrix. Utilizing this result we have obtained computationally convenient formula for the expected value of the $j$th elementary symmetric function of the roots of central positive definite quadratic form in matrix argument.
Publié le : 1974-07-14
Classification:
Noncentral Wishart matrix,
elementary symmetric function,
positive definite quadratic form in matrix argument
@article{1176342773,
author = {Shah, B. K. and Khatri, C. G.},
title = {Proof of Conjectures About the Expected Values of the Elementary Symmetric Functions of a Noncentral Wishart Matrix},
journal = {Ann. Statist.},
volume = {2},
number = {1},
year = {1974},
pages = { 833-836},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342773}
}
Shah, B. K.; Khatri, C. G. Proof of Conjectures About the Expected Values of the Elementary Symmetric Functions of a Noncentral Wishart Matrix. Ann. Statist., Tome 2 (1974) no. 1, pp. 833-836. http://gdmltest.u-ga.fr/item/1176342773/