Best Equivariant Estimators of a Cholesky Decomposition
Eaton, Morris L. ; Olkin, Ingram
Ann. Statist., Tome 15 (1987) no. 1, p. 1639-1650 / Harvested from Project Euclid
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Every positive definite matrix $\Sigma$ has a unique Cholesky decomposition $\Sigma = \theta\theta'$, where $\theta$ is lower triangular with positive diagonal elements. Suppose that $S$ has a Wishart distribution with mean $n\Sigma$ and that $S$ has the Cholesky decomposition $S = XX'$. We show, for a variety of loss functions, that $XD$, where $D$ is diagonal, is a best equivariant estimator of $\theta$. Explicit expressions for $D$ are provided.
Publié le : 1987-12-14
Classification:  Rectangular coordinates,  random matrices,  62H10,  15A52,  15A23 
@article{1176350615,
     author = {Eaton, Morris L. and Olkin, Ingram},
     title = {Best Equivariant Estimators of a Cholesky Decomposition},
     journal = {Ann. Statist.},
     volume = {15},
     number = {1},
     year = {1987},
     pages = { 1639-1650},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176350615}
}

Eaton, Morris L.; Olkin, Ingram. Best Equivariant Estimators of a Cholesky Decomposition. Ann. Statist., Tome 15 (1987) no. 1, pp.  1639-1650. http://gdmltest.u-ga.fr/item/1176350615/