 Best equivariant estimation in curved covariance modelsF. Perron and N. Giri Journal of Multivariate Analysis, 1992, vol. 40, issue 1, 46-55 Abstract: Let X1, ..., Xn (n > p > 2) be independently and identically distributed p-dimensional normal random vectors with mean vector [mu] and positive definite covariance matrix [Sigma] and let [Sigma] and . be partioned as1 p-1 1 p-1. We derive here the best equivariant estimators of the regression coefficient vector [beta] = [Sigma]22-1[Sigma]21 and the covariance matrix [Sigma]22 of covariates given the value of the multiple correlation coefficient [varrho]2 = [Sigma]11-1[Sigma]12[Sigma]22-1[Sigma]21. Such problems arise in practice when it is known that [varrho]2 is significant. Let R2 = S11-1S12S22-1S21. If the value of [varrho]2 is such that terms of order (R[varrho])2 and higher can be neglected, the best equivariant estimator of [beta] is approximately equal to (n -1)(p - 1)-1 [varrho]2S22-1S21, where S22-1S21 is the maximum likelihood estimator of [beta]. When [varrho]2 = 0, the best equivariant estimator of [Sigma]22 is (n - p + 1)-1S22 is the maximum likelihood estimator of [Sigma]22. Keywords: ancillary; statistic; curved; covariance; model; equivariant; estimator; maximal; invariant; multiple; correlation; coefficient; regression; vector (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:40:y:1992:i:1:p:46-55 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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