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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
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.
[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 10.1080/03610928008827898 | MR 0561552 | Zbl 0432.62045
[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 10.1080/03610928108828108 | MR 0625025 | Zbl 0473.62055
[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 10.1080/01621459.1967.10482895 | MR 0215439 | Zbl 0152.37201
[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 10.1080/03610928108828046 | MR 0612404
[5] J. Kleffe: Simultaneous estimation of expectation and covariance matrix in linear models. Math. Operationsforsch. Statist., Series Statistics 9(3) (1978), 443-478. MR 0522072 | Zbl 0415.62026
[6] L. Kubáček: Foundations of Estimation Theory. Volume 9 of Fundamental Studies in Engineering, first edition, Elsevier, Amsterdam, Oxford, New York, Tokyo, 1988. MR 0995671
[7] C. R. Rao: Linear Statistical Inference and Its Applications. John VViley, New York, first edition, 1973. MR 0346957 | Zbl 0256.62002
[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 0338013 | Zbl 0236.15005
[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 10.1080/03610928208828266 | MR 0651607 | Zbl 0516.62053
[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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