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January, 1978 Positive Dependence of the Roots of a Wishart Matrix
Richard L. Dykstra, John E. Hewett
Ann. Statist. 6(1): 235-238 (January, 1978). DOI: 10.1214/aos/1176344083

Abstract

It is shown that the characteristic roots of a Wishart matrix (identity covariance matrix) and the roots of $S_1 S_2^{-1}$ and $S_1(S_1 + S_2)^{-1}$ where $S_1, S_2$ are independent $p \times p$ Wishart matrices with the same covariance matrix, satisfy certain types of dependency relationships. That is, it is shown that these roots are (a) positive orthant dependent, (b) associated, (c) stochastically increasing in sequence, and (d) positively likelihood ratio dependent. An example of how this may be used in obtaining simultaneous confidence intervals is also included.

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Richard L. Dykstra. John E. Hewett. "Positive Dependence of the Roots of a Wishart Matrix." Ann. Statist. 6 (1) 235 - 238, January, 1978. https://doi.org/10.1214/aos/1176344083

Information

Published: January, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0377.62036
MathSciNet: MR458718
Digital Object Identifier: 10.1214/aos/1176344083

Subjects:
Primary: 62H99

Keywords: characteristic roots , Positive dependence , totally positive of order two , Wishart distribution

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 1 • January, 1978
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