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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)
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##### References:
 [1] ANDERSON T. W.: Introduction to Multivariate Statistical Analysis. J. Wiley, N. York 1958. · Zbl 0083.14601 [2] KUBÁČEK L.: Regression model with estimated covariance matrix. Math. Slovaca 33, 1983, 395-408. · Zbl 0524.62067 [3] LEHMANN E. L., SCHEFFÉ H.: Completeness, similar regions and unbiased estimation - Part I. Sankhya 10, 1950, 306-340. · Zbl 0041.46301 [4] RAO C. R.: Estimation of variance and covariance components-MINQUE theory. Journ. Multivariat. Analysis 1, 1971, 257-275. · Zbl 0223.62086 [5] RAO C. R., MITRA K. S.: Generalized Inverse of Matrices and its Application. J. Wiley, N. York 1971. · Zbl 0236.15004 [6] RAO C. R., KLEFFE J.: Estimation of Variance Components. Krisnaiah, P. R. Handbook of Statistics, Vol. I. 1-40, North Holland, N. York 1980. . · Zbl 0476.62058 [7] SEELY J.: Linear spaces and unbiased estimation. Ann. Math. Statistics, 41, 1971, 1725-1734. · Zbl 0263.62040 [8] SEELY J.: Linear spaces and unbiased estimation - application to the mixed linear model. Ann. Math. Statistics, 41, 1970, 1735-1748. · Zbl 0263.62041
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