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Distribution of multivariate quadratic forms under certain covariance structures
Author(s) -
Pavur Robert J.
Publication year - 1987
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315206
Subject(s) - wishart distribution , covariance , mathematics , rational quadratic covariance function , multivariate statistics , estimation of covariance matrices , multivariate normal distribution , law of total covariance , matérn covariance function , statistics , covariance matrix , quadratic equation , covariance function , matrix t distribution , population , covariance intersection , geometry , demography , sociology
Necessary and sufficient conditions are given for the covariance structure of all the observations in a multivariate factorial experiment under which certain multivariate quadratic forms are independent and distributed as a constant times a Wishart. It is also shown that exact multivariate test statistics can be formed for certain covariance structures of the observations when the assumption of equal covariance matrices for each normal population is relaxed. A characterization is given for the dependency structure between random vectors in which the sample mean and sample covariance matrix have certain properties.