Sphericity and the Normal Law
Berk, Robert H.
Ann. Probab., Tome 14 (1986) no. 4, p. 696-701 / Harvested from Project Euclid
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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.
Publié le : 1986-04-14
Classification:  Characterization of normality,  sphericity,  sufficiency,  least-squares estimator,  60E99,  62B99 
@article{1176992538,
     author = {Berk, Robert H.},
     title = {Sphericity and the Normal Law},
     journal = {Ann. Probab.},
     volume = {14},
     number = {4},
     year = {1986},
     pages = { 696-701},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992538}
}

Berk, Robert H. Sphericity and the Normal Law. Ann. Probab., Tome 14 (1986) no. 4, pp.  696-701. http://gdmltest.u-ga.fr/item/1176992538/