## Annals of Probability

### Sphericity and the Normal Law

Robert H. Berk

#### Abstract

Let $\mathbf{x} = (x_1,\cdots, x_n)'$ be a random vector in $R^n$. Two characterizations of normality are given. One involves the existence of two linear combinations of the $\{x_j\}$ that are independent in every coordinate system. The other, which is actually a consequence of the first, assumes that $\mathbf{x}$ obeys a linear model with spherical errors and involves sufficiency of the least-squares estimator.

#### Article information

Source
Ann. Probab., Volume 14, Number 2 (1986), 696-701.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992538

Digital Object Identifier
doi:10.1214/aop/1176992538

Mathematical Reviews number (MathSciNet)
MR832031

Zentralblatt MATH identifier
0595.60016

JSTOR