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Unbiasedness of the Estimator of the Function of Expected Value in the Mixed Linear Model
Author(s) -
Klaczyński K.,
Molińska A.,
Moliński K.
Publication year - 1994
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.4710360211
Subject(s) - mathematics , estimator , linear model , variance function , generalized linear mixed model , statistics , generalized least squares , linear least squares , rank (graph theory) , combinatorics
The traditional method for estimating the linear function of fixed parameters in mixed linear model is a two‐stage procedure. In the first stage of this procedure the variance components estimators are calculated and next in the second stage these estimators are taken as true values of variance components to estimating the linear function of fixed parameters according to generalized least squares method. In this paper the general mixed linear model is considered in which a matrix related to fixed parameters and or/a dispersion matrix of observation vector may be deficient in rank. It is shown that the estimators of a set of functions of fixed parameters obtained in second stage are unbiased if only the observation vector is symmetrically distributed about its expected value and the estimators of variance components from first stage are translation‐invariant and are even functions of the observation vector.