## The Annals of Statistics

### Testing for Ellipsoidal Symmetry of a Multivariate Density

Rudolf Beran

#### Abstract

Let $Z$ be a random vector whose distribution is spherically symmetric about the origin. A random vector $X$ which is representable as the image of $Z$ under affine transformation is said to have an ellipsoidally symmetric distribution. The model of ellipsoidal symmetry is a useful generalization of multivariate normality. This paper proposes and studies some goodness-of-fit tests which have good asymptotic power over a broad spectrum of alternatives to ellipsoidal symmetry.

#### Article information

Source
Ann. Statist., Volume 7, Number 1 (1979), 150-162.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176344561

Digital Object Identifier
doi:10.1214/aos/1176344561

Mathematical Reviews number (MathSciNet)
MR515690

Zentralblatt MATH identifier
0406.62029

JSTOR