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.


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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