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Analysis of Covariance in Split Block Design
Author(s) -
Kuczyński M.
Publication year - 1982
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.4710240709
Subject(s) - mathematics , estimator , statistics , covariance matrix , minimum variance unbiased estimator , covariance , bias of an estimator , identity matrix , best linear unbiased prediction , stein's unbiased risk estimate , linear model , efficient estimator , computer science , eigenvalues and eigenvectors , physics , quantum mechanics , artificial intelligence , selection (genetic algorithm)
In this paper the analysis of covariance in the split block design with many concomitant variables is presented. The problems concerning the estimation of parametric functions and testing hypotheses are discussed. In the presentation of the model three kinds of regression coefficients for individual sources of variation are taken into consideration. It is shown that for every estimable function of fixed effects, the best linear unbiased estimator under the assumed model is the same as the best linear unbiased estimator under the model with covariance matrix equal to identity matrix multiplied by a positive constant. A variance of this estimator can be calculated by the method presented here. Test functions for standard hypotheses concerning fixed effects are obtained.