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MINQUE and ANOVA Estimator for One‐way Classification ‐ a Risk Comparison
Author(s) -
Ahrens H.
Publication year - 1978
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710200602
Subject(s) - mathematics , analysis of variance , statistics , estimator , repeated measures design
For the one‐way classification in unbalanced case MINQUEstimator for components of variance are given in a more explicit form than it is done in the paper from C. R. RAO (1971). By means of the risk functions we compare MINQUE and ANOVA estimator. For given n j ‐patterns angular ranges in the positive quadrant are given where MINQUE is better than ANOVA estimator. A special n j ‐pattern and one parameter δ 0 is found for which MINQUE is uniformly better than ANOVA. Limit values are given for MINQUE for δ 0 = ∞ and δ 0 = 0 and their relations to the ANOVA estimator are considered. The coincidence between MINQUE and ANOVA for balanced case is verified. Extensive numerical studies for real data are carried out which stimulated the search for a fixpoint δ as a point for which the distance to the initial parameter δ 0 is as small as possible.