Unbiasedness of the Estimator of the Function of Expected Value in the Mixed Linear Model

✍ Scribed by K. Klaczyński; A. Molińska; K. Moliński

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 328 KB
• Volume: 36
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710360211

✦ Synopsis

The traditional method for estimating the linear function of fiied parameters in mixed linear model is a two-stage p r d u r e . 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 variana components from first stage are translation-invm'ant and are even functions of the observation vector.