## The Annals of Statistics

### Positive Dependence of the Roots of a Wishart Matrix

#### 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.

#### Article information

Source
Ann. Statist., Volume 6, Number 1 (1978), 235-238.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176344083

Digital Object Identifier
doi:10.1214/aos/1176344083

Mathematical Reviews number (MathSciNet)
MR458718

Zentralblatt MATH identifier
0377.62036

JSTOR