Maximum likelihood estimation of Wishart mean matrices under Löwner order restrictions

Ming-Tien Tsai

Journal of Multivariate Analysis, 2007, vol. 98, issue 5, 932-944

Abstract: For Wishart density functions, there remains a long-time question unsolved. That is whether there exists the closed-form MLEs of mean matrices over the partially Löwner ordering sets. In this note, we provide an affirmative answer by demonstrating a unified procedure on exactly how the closed-form MLEs are obtained for the simple ordering case. Under the Kullback-Leibler loss function, a property of obtained MLEs is further studied. Some applications of the obtained closed-form MLEs, including the comparison between our ML estimates and Calvin and Dykstra's [Maximum likelihood estimation of a set of covariance matrices under Löwner order restrictions with applications to balanced multivariate variance components models, Ann. Statist. 19 (1991) 850-869.] which obtained by iterative algorithm, are also made.

Keywords: Exterior; differential; forms; Matrix; factorizations; Kullback-Leibler; loss; function; Simple; ordering; set; Wishart; density; function (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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