Distribution of multivariate quadratic forms under certain covariance structures

DOI10.2307/3315206zbMath0626.62050OpenAlexW1971168990MaRDI QIDQ3030028

Robert J. Pavur

Publication date: 1987

Published in: Canadian Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/3315206

zbMATH Keywords

Wishart distributioncovariance structuresample meandependency structureNecessary and sufficient conditionsnormal populationmultivariate quadratic formsexact multivariate test statisticstranslational invariant

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Factorial statistical designs (62K15)

Related Items (16)

Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures ⋮ Independence-distribution-preserving dependency structures for the modified likelihood ratio test for detecting unequal covariance matrices ⋮ Cochran theorems for a multivariate elliptically contoured model ⋮ Independence distribution preserving joint covariance structures for the multivariate two-group case ⋮ Versions of Cochran's theorem for general quadratic expressions in normal matrices ⋮ Wishart and chi-square distributions associated with matrix quadratic forms ⋮ Probabilistic multidimensional scaling: An anisotropic model for distance judgments ⋮ A brief derivation of necessary and sufficient conditions for a family of matrix quadratic forms to have mutually independent non-central Wishart distributions ⋮ Conditions for invariance of the multivariate versions of Grubb's test and Bartlett's test under a general dependency structure ⋮ Multivariate versions of Cochran's theorems ⋮ 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 ⋮ A decomposition for a stochastic matrix with an application to MANOVA ⋮ Cochran theorems for a multivariate vector-elliptically contoured model. II ⋮ A characterization of the independence - distribution - preserving covariance structure for the multivariate maximum squared - radii statistic

Cites Work

• On the robustness of least squares procedures in regression models
• Testing regression function adequacy with correlation and without replication
• Unbiased F Tests for Factorial Experiments for Correlated Data
• Multivariate Analysis of Variance in a Randomized Blocks Design when Covariance Matrices are Unequal
• On Independence of Sample Mean and Translation Invariant Statistics of Samples from Multivariate Normal Populations
• Necessary and Sufficient Conditions for F Ratios in the L × J × K Factorial Design with Two Repeated Factors
• Conditions Under Which Mean Square Ratios in Repeated Measurements Designs Have Exact F-Distributions
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