Binary operations on Jordan algebras: An application to statistical inference in linear models
Ricardo Covas, Roman Zmyślony, Francisco Carvalho · AIP conference proceedings · 2012
Necessary and sufficient conditions for the existence of best unbiased estimators (UMVUE) in Normal Linear Mixed Models, Y∼N(Xβ, ∑ i = 1kσi2Vi), are given. These conditions rely on the existence of Jordan algebras, in the sequence of [19], [6], [9], [7], [3] and [8]. We also take [2] in mind where lattices of Jordan algebras are presented for estimation purposes in these models and [1] where such estimation is exemplified.