Multivariate versions of Cochran's theorems

DOI10.1016/0047-259X(91)90011-PzbMath0749.62037OpenAlexW4213178627MaRDI QIDQ1182753

Joe Masaro, Chi Song Wong, Tonghui Wang

Publication date: 28 June 1992

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0047-259x(91)90011-p

zbMATH Keywords

inclusion mapgeneralized inverseWishart distributioninner product spacesnecessary and sufficient conditionorthogonal projectionouter productself-adjoint operatorslinear mapscharacteristic functions of random quadratic mapsindependent family of Wishart random operatorsmultivariate versions of Cochran theorems

Mathematics Subject Classification ID

Characterization and structure theory for multivariate probability distributions; copulas (62H05) Quadratic and bilinear forms, inner products (15A63) Basic linear algebra (15A99) Vector spaces, linear dependence, rank, lineability (15A03) Probability theory on linear topological spaces (60B11)

Related Items (21)

Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures ⋮ Estimating covariance in a growth curve model ⋮ Cochran theorems for a multivariate elliptically contoured model ⋮ Versions of Cochran's theorem for general quadratic expressions in normal matrices ⋮ Wishart and chi-square distributions associated with matrix quadratic forms ⋮ A simplified version of Cochran's theorem in mixed linear models ⋮ Distribution of matrix quadratic forms under skew-normal settings ⋮ Nonnegative definite solutions to matrix equations with applications to multivariate test statis\-tics ⋮ Wishartness and independence of matrix quadratic forms in a normal random matrix ⋮ Wishart-Laplace distributions associated with matrix quadratic forms ⋮ Sampling distributions of skew normal populations associated with closed skew normal distributions ⋮ A decomposition for a stochastic matrix with an application to MANOVA ⋮ Equivalent conditions for noncentral generalized Laplacianness and independence of matrix quadratic forms ⋮ Estimation in a growth curve model with singular covariance ⋮ Wishart distributions associated with matrix quadratic forms ⋮ Independence distribution preserving covariance structures for the multivariate linear model ⋮ Cochran theorems for a multivariate vector-elliptically contoured model. II ⋮ Multivariate versions of Cochran theorems ⋮ Nonnegative definite and re-nonnegative definite solutions to a system of matrix equations with statistical applications ⋮ Evaluating matrix-variate moments through higher-order differential forms and combinatorial algorithms. ⋮ The Decomposition of Quadratic Forms Under Matrix Variate Skew-Normal Distribution

Cites Work

• On the use of differentials in statistics
• Characterizations of products of symmetric matrices
• Projections, generalized inverses, and quadratic forms
• Distribution of multivariate quadratic forms under certain covariance structures
• Conditions for Wishartness and Independence of Second Degree Polynomials in a Normal Vector
• Some Matrix Results and Extensions of Cochran’s Theorem
• Conditions for a quadratic form to have a chi-squared distribution
• Linear Statistical Inference and its Applications
• Notes on the distribution of quadratic forms in singular normal variables
• On the Distribution of General Quadratic Functions in Normal Vectors
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