The Annals of Statistics

Proof of Conjectures About the Expected Values of the Elementary Symmetric Functions of a Noncentral Wishart Matrix

B. K. Shah and C. G. Khatri

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Abstract

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.

Article information

Source
Ann. Statist., Volume 2, Number 4 (1974), 833-836.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342773

Digital Object Identifier
doi:10.1214/aos/1176342773

Mathematical Reviews number (MathSciNet)
MR362716

Zentralblatt MATH identifier
0285.62026

JSTOR
links.jstor.org

Keywords
Noncentral Wishart matrix elementary symmetric function positive definite quadratic form in matrix argument

Citation

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. 2 (1974), no. 4, 833--836. doi:10.1214/aos/1176342773. https://projecteuclid.org/euclid.aos/1176342773


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