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Repeated regression experiment and estimation of variance components. (English) Zbl 0597.62051

In the regression model \(Y=X\beta +\epsilon\) the covariance matrix of the vector \(\epsilon\) (i.e. the covariance matrix of the random vector Y) is considered in the form \(\Sigma =\nu_ 1V_ 1+...+\nu_ mV_ m\); \(\nu_ 1,...,\nu_ m\) are variance components. The aim is to estimate the components \(\nu_ 1,...,\nu_ m\) on the basis of the \((k+1)\)-tuple stochastically independent realizations of a normally distributed vector \(Y\sim N_ n(X\beta,\Sigma)\), when the matrix X and the symmetric matrices \(V_ 1,...,V_ m\) are known. The vector \(\beta\) is a nuisance parameter.

MSC:

62H12 Estimation in multivariate analysis
62J10 Analysis of variance and covariance (ANOVA)

Citations:

Zbl 0597.62052
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References:

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