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Keywords:
ellipsoidal restrictions
ellipsoidal restrictions
Summary:
The paper deals with modified minimax quadratic estimation of variance and covariance components under full ellipsoidal restrictions. Based on the, so called, linear approach to estimation variance components, i. e. considering useful local transformation of the original model, we can directly adopt the results from the linear theory. Under normality assumption we can can derive the explicit form of the estimator which is formally find to be the Kuks–Olman type estimator.
References:
[1] Gaffke N., Heiligers B.: Bayes, admissible, and minimax linear estimators in linear models with restricted parameter space. Statistics 20 (1989), 4, 487–508 DOI 10.1080/02331888908802199 | MR 1047218 | Zbl 0686.62019
[2] Heiligers B.: Linear Bayes and minimax estimation in linear models with partially restricted parameter space. J. Statist. Plann. Inference 36 (1993), 175–184 DOI 10.1016/0378-3758(93)90122-M | MR 1234847 | Zbl 0780.62027
[3] Kozák J.: Modified minimax estimation of regression coefficients. Statistics 16 (1985), 363–371 DOI 10.1080/02331888508801866 | MR 0792078 | Zbl 0588.62108
[4] Kubáček L., Kubáčková L., Volaufová J.: Statistical Models with Linear Structures. Publishing House of the Slovak Academy of Sciences, Bratislava 1995
[5] Pilz J.: Minimax linear regression estimation with symmetric parameter restrictions. J. Statist. Plann. Inference 13 (1986), 297–318 DOI 10.1016/0378-3758(86)90141-2 | MR 0835614 | Zbl 0602.62054
[6] Pukelsheim F.: Estimating variance components in linear models. J. Multivariate Anal. 6 (1976), 626–629 DOI 10.1016/0047-259X(76)90010-5 | MR 0438602 | Zbl 0355.62061
[7] Rao C. R.: Estimation of variance and covariance components – MINQUE theory. J. Multivariate Anal. 1 (1971), 257–275 DOI 10.1016/0047-259X(71)90001-7 | MR 0301869 | Zbl 0223.62086
[8] Rao C. R.: Minimum variance quadratic unbiased estimation of variance components. J. Multivariate Anal. 1 (1971), 445–456 DOI 10.1016/0047-259X(71)90019-4 | MR 0301870 | Zbl 0259.62061
[9] Rao C. R.: Unified theory of linear estimation. Sankhyā Ser. B 33 (1971), 371–394 MR 0319321 | Zbl 0236.62048
[10] Rao C. R., Kleffe J.: Estimation of Variance Components and Applications. Statistics and Probability, Volume 3. North–Holland, Amsterdam – New York – Oxford – Tokyo 1988 MR 0933559 | Zbl 0645.62073
[11] Rao C. R., Mitra K.: Generalized Inverse of Matrices and Its Applications. Wiley, New York – London – Sydney – Toronto 1971 MR 0338013 | Zbl 0261.62051
[12] Searle S. R., Casella, G., McCulloch, Ch. E.: Variance Components. (Wiley Series in Probability and Mathematical Statistics.) Wiley, New York – Chichester – Brisbane – Toronto – Singapore 1992 MR 1190470 | Zbl 1108.62064
[13] Volaufová J.: A brief survey on the linear methods in variance-covariance components model. In: Model–Oriented Data Analysis (W. G. Müller, H. P. Wynn, and A. A. Zhigljavsky, eds.), Physica–Verlag, Heidelberg 1993, pp. 185–196 MR 1281860
[14] Volaufová J., Witkovský V.: Estimation of variance components in mixed linear model. Appl. Math. 37 (1992), 139–148
[15] Zyskind G.: On canonical forms, nonnegative covariance matrices and best and simple least square estimator in linear models. Ann. Math. Statist. 38 (1967), 1092–1110 DOI 10.1214/aoms/1177698779 | MR 0214237
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