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Estimation in a growth curve model with singular covariance. (English) Zbl 1015.62056

Summary: Let \(Y\) be a multivariate normal random matrix with covariance \(A\otimes\Sigma\) and mean \(\mu\in S_1S_2'\), where \(S_i=\{X_i b_i: K_i'b_i= M_i'u_i\) for some \(u_i\}\) and \(S_1S_2'\) is the linear span of the set of all \(x_1x_2'\) with \(x_i\in S_i\). Explicit formulae are obtained for the estimators of \((\mu,\Sigma)\). These estimators are investigated through a large class of loss functions and other principles. None of the matrices \(A,\Sigma, X_i,K_i\) and \(M_i\) are assumed to have full column rank. For robust studies, elliptical \(Y\) is considered when it is appropriate.

MSC:

62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
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