## The Annals of Statistics

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

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

Richard L. Dykstra and John E. Hewett

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 62H99: None of the above, but in this section

**Keywords**

Wishart distribution characteristic roots positive dependence totally positive of order two

#### Citation

Dykstra, Richard L.; Hewett, John E. Positive Dependence of the Roots of a Wishart Matrix. Ann. Statist. 6 (1978), no. 1, 235--238. doi:10.1214/aos/1176344083. https://projecteuclid.org/euclid.aos/1176344083