On some pattern-reduction matrices which appear in statistics

DOI10.1016/0024-3795(85)90199-5zbMath0578.62063OpenAlexW1999909246MaRDI QIDQ1066593

Douglas P. Wiens

Publication date: 1985

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(85)90199-5

zbMATH Keywords

Kronecker productsmaximum likelihoodellipsoidal confidence regionsderivatives of matrix-valued functionsDerivatives of patterned matricesJacobians of transformationsrobust M-estimatorsvec permutation matrix

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Multivariate analysis (62H99) Estimation in multivariate analysis (62H12) Calculus of vector functions (26B12) Basic linear algebra (15A99) Canonical forms, reductions, classification (15A21)

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Cites Work

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• The commutation matrix: Some properties and applications
• Matrix derivatives with chain rule and rules for simple, Hadamard, and Kronecker products
• Matrix derivatives with an application to an adaptive linear decision problem
• On some test criteria for covariance matrix
• On Jacobians of transformations with skew-symmetric, strictly (lower) triangular or diagonal matrix arguments
• Some results on commutation matrices, with statistical applications
• Ellipsoidal confidence regions for a normal covariance matrix
• Vec and vech operators for matrices, with some uses in jacobians and multivariate statistics
• The vec-permutation matrix, the vec operator and Kronecker products: a review
• The Elimination Matrix: Some Lemmas and Applications
• Radial estimates and the test for sphericity
• Symmetric Matrix Derivatives with Applications
• On direct product matrices
• On Multivariate Distribution Theory