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April, 1986 Sphericity and the Normal Law
Robert H. Berk
Ann. Probab. 14(2): 696-701 (April, 1986). DOI: 10.1214/aop/1176992538


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.


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Robert H. Berk. "Sphericity and the Normal Law." Ann. Probab. 14 (2) 696 - 701, April, 1986.


Published: April, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0595.60016
MathSciNet: MR832031
Digital Object Identifier: 10.1214/aop/1176992538

Primary: 60E99
Secondary: 62B99

Keywords: Characterization of normality , least-squares estimator , sphericity , sufficiency

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 2 • April, 1986
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