## The Annals of Mathematical Statistics

### The Moments of Elementary Symmetric Functions of the Roots of a Matrix in Multivariate Analysis

Tito A. Mijares

#### Abstract

Pillai and Mijares [7] gave the exact expressions for the first four moments of the sum of $s$ non-zero roots of a matrix occurring in multivariate normal analysis as studied independently by R. A. Fisher [3], P. L. Hsu [4] and S. N. Roy [9]. In this paper some properties of completely homogeneous symmetric functions and certain determinantal results (Section 2) are used to give an inverse derivation of those moments (Section 4). The method is further extended to the moments in general of elementary symmetric functions (e.s.f.) of the roots of a matrix in multivariate analysis (Section 6) through the use of certain properties of compound matrices (Section 5).

#### Article information

Source
Ann. Math. Statist., Volume 32, Number 4 (1961), 1152-1160.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177704853

Digital Object Identifier
doi:10.1214/aoms/1177704853

Mathematical Reviews number (MathSciNet)
MR130751

Zentralblatt MATH identifier
0122.36905

JSTOR