Listy Biometryczne - Biometrical Letters Vol. 35(1998), No. 1, 11-26
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ON ADMISSIBILITY OF THE INTRA-BLOCK AND INTER-BLOCK VARIANCE COMPONENT ESTIMATORS Tadeusz Caliński1, Stanisław Gnot2* and Andrzej Michalski 3 1 Department of Mathematical and Statistical Methods, Agricultural University of Poznań, Wojska Polskiego 28, 60-637 Poznań, Poland 2 Institute of Mathematics, Pedagogical University, Pl. Słowiański 9, 65-069 Zielona Góra, Poland 3Department of Mathematics, Agricultural University of Wrocław, Grunwaldzka 53, 50-357 Wrocław, Poland |
In the paper the problem of admissibility of two kinds of estimators of the variance components appearing in the randomization model used for experiments in block designs is considered. It is proved, that the intra-block estimator of the variance of errors is admissible in the class of unbiased estimators. Sufficient conditions are given, for which the inter-block estimator of the variance of block effects is admissible. The conditions arę given in terms of the incidence matrix of the design. Some examples of models for which this inter-block estimator is inadmissible are presented. In such cases it is shown how to improve uniformly the estimator by using one of the admissible estimators.
admissibility, block designs, estimators of variance components, inter-and intra-block estimation, invariant quadratic unbiased estimators
