Geodesic
On variance of the two-stage estimator in variance-covariance components model
Applications of Mathematics, Tome 38 (1993) no. 1, pp. 1-9

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The paper deals with a linear model with linear variance-covariance structure, where the linear function of the parameter of expectation is to be estimated. The two-stage estimator is based on the observation of the vector $Y$ and on the invariant quadratic estimator of the variance-covariance components. Under the assumption of symmetry of the distribution and existence of finite moments up to the tenth order, an approach to determining the upper bound for the difference in variances of the estimators is proposed, which uses the estimated covariance matrix instead of the real one.
The paper deals with a linear model with linear variance-covariance structure, where the linear function of the parameter of expectation is to be estimated. The two-stage estimator is based on the observation of the vector $Y$ and on the invariant quadratic estimator of the variance-covariance components. Under the assumption of symmetry of the distribution and existence of finite moments up to the tenth order, an approach to determining the upper bound for the difference in variances of the estimators is proposed, which uses the estimated covariance matrix instead of the real one.
DOI : 10.21136/AM.1993.104529
Classification : 62F10, 62J05, 62J10
Keywords: two-stage estimator; symmetrically distributed estimator; unbiased estimator; linear variance- covariance structure; invariant quadratic estimator of the variance-covariance components; finite moments up to the tenth order; estimated covariance matrix 
Volaufová, Júlia. On variance of the two-stage estimator in variance-covariance components model. Applications of Mathematics, Tome 38 (1993) no. 1, pp. 1-9. doi: 10.21136/AM.1993.104529
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[1] F. J. H. Don, J.R. Magnus: On the unbiasedness of iterated GLS estimators. Commun. Statist.-Theory Meth. A9(5) (1980), 519-527. | DOI | MR | Zbl

[2] R.N. Kackar, D. A. Harville: Unbiasedness of two-stage estimation and prediction procedures for mixed linear models. Commun. Statist.-Theory Meth. A10(3) (1981), 1249-1261. | DOI | MR | Zbl

[3] N.C. Kakwani: The unbiasedness of Zellner's seemingly unrelated regression equations estimators. Journal of the American Statistical Association 67 (1967), 141-142. | DOI | MR | Zbl

[4] C.G. Khatri, K.R. Shah: On the unbiased estimation of fixed effects in a mixed model for growth curves. Commun. Statist.-Theory Meth. A 10(4) (1980), 401-406. | DOI | MR

[5] J. Kleffe: Simultaneous estimation of expectation and covariance matrix in linear models. Math. Operationsforsch. Statist., Series Statistics 9(3) (1978), 443-478. | MR | Zbl

[6] L. Kubáček: Foundations of Estimation Theory. Volume 9 of Fundamental Studies in Engineering, first edition, Elsevier, Amsterdam, Oxford, New York, Tokyo, 1988. | MR

[7] C. R. Rao: Linear Statistical Inference and Its Applications. John VViley, New York, first edition, 1973. | MR | Zbl

[8] C. R. Rao, S. K. Mitra: Generalized Inverse of Matrices and Its Applications. first edition, John Wiley &; Sons, New York, London, Sydney, Toronto, 1971. | MR | Zbl

[9] J. Seely, R. V. Hogg: Symmetrically distributed and unbiased estimators in linear models. Commun. Statist.-Theory Meth. A 11(7) (1982), 721-729. | DOI | MR | Zbl

[10] J. Volaufová V. Witkovský, and M. Bognárová: On the confidence region of parameter of mean in mixed linear models. Poster at European meeting of Statisticians, Berlin, August 1988.

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