Annals of Probability

Sphericity and the Normal Law

Robert H. Berk

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60E99: None of the above, but in this section
Secondary: 62B99: None of the above, but in this section

Keywords
Characterization of normality sphericity sufficiency least-squares estimator

Citation

Berk, Robert H. Sphericity and the Normal Law. Ann. Probab. 14 (1986), no. 2, 696--701. doi:10.1214/aop/1176992538. https://projecteuclid.org/euclid.aop/1176992538


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