Cochran's statistical theorem revisited

DOI10.1016/j.jspi.2004.09.016zbMath1094.15003OpenAlexW2062901232MaRDI QIDQ2495833

Yongge Tian, George P. H. Styan

Publication date: 30 June 2006

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2004.09.016

zbMATH Keywords

idempotent matricesrank subtractivityrank additivityrank formulas for partitioned matricesrank equalitiesChi-squared distributionquadratic forms in normal variablesmatrix version of Cochran's theorem

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24)

Related Items (8)

A simplified version of Cochran's theorem in mixed linear models ⋮ Extremal ranks of matrix expression of \(A - BXC\) with respect to Hermitian matrix ⋮ A study of wavelet analysis and data extraction from second-order self-similar time series ⋮ On additive and block decompositions of WLSEs under a multiple partitioned regression model ⋮ Method of elementary transformation to compute Moore-Penrose inverse ⋮ Some equalities for estimations of variance components in a general linear model and its restricted and transformed models ⋮ Miscellaneous equalities for idempotent matrices with applications ⋮ On the equivalence of estimations under a general linear model and its transformed models

Cites Work

• A further algebraic version of Cochran's theorem and matrix partial orderings
• On a matrix version of Cochran's statistical theorem
• Properties of normalr-potent matrices
• Some results concerning normalr- potent operators
• Some Matrix Results and Extensions of Cochran’s Theorem
• On the distribution of quadratic forms in normal random variables
• Characterizations of r-potent matrices
• Notes on the distribution of quadratic forms in singular normal variables
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