Eaton, Morris L.; Olkin, Ingram Best equivariant estimators of a Cholesky decomposition. (English) Zbl 0629.62057 Ann. Stat. 15, 1639-1650 (1987). 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. Cited in 1 ReviewCited in 18 Documents MSC: 62H12 Estimation in multivariate analysis 15A23 Factorization of matrices 62H10 Multivariate distribution of statistics 62A01 Foundations and philosophical topics in statistics 15B52 Random matrices (algebraic aspects) Keywords:rectangular coordinates; Cholesky decomposition; Wishart distribution; loss functions; best equivariant estimator × Cite Format Result Cite Review PDF Full Text: DOI