On admissibility of linear estimators in models with finitely generated parameter space

An explicit characterization of admissible linear estimators of fixed and random effects in balanced random models

“…So the first part of the proof is completed by using a result of LaMotte [15] that each linear estimator of K E Y admissible among L 0 is a limit of members of L 0 that are uniquely best among L 0 in T . Sufficiency follows straightforwardly from a result of Synówka-Bejenka and Zontek [26] that for a model with finitely generated parameter space each limit of members of L 0 is admissible.…”

“…Basing on LaMotte's results [13] Synówka-Bejenka and Zontek [26] have proved that for linear models with finitely generated parameter space every limit of a sequence of ULBEs is admissible. To prove that, they applied a stepwise procedure of LaMotte [13].…”

“…Further results on unbiased estimation of both kinds of effects were obtained, among others, by Goldberger [4], Henderson ([8], [9]), Harville [6], Rao [19], Jiang [10], Liu et al [16] and Tian [27]. Synówka-Bejenka and Zontek ( [25], [26]) have dealt with admissibility of linear estimators of fixed and random effects in some linear models. To get a characterization, they have shown that the problem of admissibility for a linear function of fixed and random effects is equivalent to the problem of admissibility for a linear function of the expected value only, in another properly defined linear model (called the dual model; see Section 3 for more details).…”

Characterization of admissible linear estimators under extended balanced loss function

“…Some important examples are given as follows: Baksalary and Markiewicz [1,2,3], Klonecki and Zontek [14], Stepniak [20], Hoffmann [13], Markiewicz [17], Yu Lu and Zhong Shi [26], Groß and Markiewicz [12]. Recently, Synowka Bejenka and Zontek [24] examined on admissibility of linear estimators in models with finitely generated parameter space.…”