Autore
Tian, Yongge

Titolo
Transformation approaches of linear random-effects models
Periodico
Statistical methods & applications : Journal of the Italian Statistical Society
Anno: 2017 - Volume: 26 - Fascicolo: 4 - Pagina iniziale: 583 - Pagina finale: 608

Assume that a linear random-effects model y=Xββ+εε=X(Aαα+γγ)+εε is transformed as Ty=TXββ+Tεε=TX(Aαα+γγ)+Tεε by pre-multiplying a given matrix T of arbitrary rank. These two models are not necessarily equivalent unless T is of full column rank, and we have to work with this derived model in many situations. Because predictors/estimators of the parameter spaces under the two models are not necessarily the same, it is primary work to compare predictors/estimators in the two models and to establish possible links between the inference results obtained from two models. This paper presents a general algebraic approach to the problem of comparing best linear unbiased predictors (BLUPs) of parameter spaces in an original linear random-effects model and its transformations, and provides a group of fundamental and comprehensive results on mathematical and statistical properties of the BLUPs. In particular, we construct many equalities for the BLUPs under an original linear random-effects model and its transformations, and obtain necessary and sufficient conditions for the equalities to hold.



SICI: 1618-2510(2017)26:4<583:TAOLRM>2.0.ZU;2-T

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