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Testing for the Equality of the Variance‐Covariance Matrices of Two Jointly Normal Vector Variables
Author(s) -
Smith Patricia L.,
Kshiesagar Anant M.
Publication year - 1985
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710270514
Subject(s) - mathematics , covariance , multivariate normal distribution , variance (accounting) , covariance matrix , statistics , restricted maximum likelihood , likelihood ratio test , combinatorics , random variate , maximum likelihood , random variable , multivariate statistics , accounting , business
Assume a joint 2P ‐variate normal distribution for the p ‐component vectors x and y with unknown mean and unknown variance‐covariance matrices Σ xx and Σ yy respectively, with Cov ( x , y )=Σ xy . No assumptions are made about the nature of Σ xy . The likelihood ratio method is investigated to test the hypothesis that Σ xx = Σ yy . A method of numerical solution to the likelihood equations in the restricted parameter case is given when p =2, and approximate solutions are suggested for p >2.