×

zbMATH — the first resource for mathematics

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)
PDF BibTeX XML Cite
Full Text: EuDML
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.