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ML estimation and LR tests for the multivariate normal distribution with general linear model mean and linear-structure covariance matrix: K- population, complete-data case. (English) Zbl 0602.62043

The K-population multivariate normal distribution with linear structure in both the mean and covariance matrix, \[ Y_{di}\sim NID_{p_ d}[\mu_ d=X_ d\beta,\Sigma_ d=\Sigma_ g\tau_ gG_{gd}] \] is examined. Maximum likelihood (ML) estimators of the parameters \(\tau^ T=(\tau_ 1,...,\tau_ m)\) and \(\beta\) are derived, for unconstrained parameters and when the parameters are constrained by (i) \(L^ T\beta =\theta_ 0\); (ii) \(S^ T\tau =\gamma_ 0\); and, (iii) by both (i) and (ii). Algorithms for solving the likelihood equations are discussed. Asymptotic distributions of the ML estimators and asymptotic efficiency are shown. Likelihood ratio (LR) tests of null hypotheses corresponding to (i), (ii), and (iii) are obtained and the asymptotic null and non-null distributions (for a series of local alternative hypotheses) of the LR test statistics are presented.

MSC:

62H12 Estimation in multivariate analysis
62H15 Hypothesis testing in multivariate analysis
62H10 Multivariate distribution of statistics
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