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Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model. (English) Zbl 0818.62017

Summary: Three results are given presenting asymptotically normal confidence intervals for the determinant \(| \sigma^ 2 \Sigma|\) in the multivariate Gauss-Markov model \((U, XB, \sigma^ 2 \Sigma\otimes V)\), \(\Sigma>0\), scalar \(\sigma^ 2>0\), with a matrix \(V\geq 0\). A known \(n\times p\) random matrix \(U\) has the expected value \(E (U)= XB\), where the \(n\times d\) matrix \(X\) is a known matrix of an experimental design, \(B\) is an unknown \(d\times p\) matrix of parameters and \(\sigma^ 2 \Sigma\otimes V\) is the covariance matrix of \(U\), \(\otimes\) being the symbol for the Kronecker product of matrices.

MSC:

62E20 Asymptotic distribution theory in statistics
62F25 Parametric tolerance and confidence regions
62H10 Multivariate distribution of statistics
62J99 Linear inference, regression
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References:

[1] T.W. Anderson: Introduction to Multivariate Statistical Analysis. J. Wiley, New York, 1958. · Zbl 0083.14601
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