Analysis of transformations of linear random-effects models
نویسنده
چکیده
Assume that a linear random-effects model (LRM) y = Xβ +ε = Xβ +ε with β = Aα+γ is transformed as Ty = TXβ + Tε = TXAα + TXγ + Tε by pre-multiplying a given matrix T. Estimations/predictions of the unknown parameters under the two models are not necessarily the same because the transformation matrix T occurs in the statistical inference of the transformed model. This paper presents a general algebraic approach to the problem of best linear unbiased prediction (BLUP) of a joint vector all unknown parameters in the LRM and its linear transformations, and provides a group of fundamental and comprehensive results on mathematical and statistical properties of the BLUP under the LRM. Mathematics Subject Classifications: 62J05; 62H12
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