On the structure of admissible linear estimators

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

“…Basing on algebraic properties of matrices Cohen [3] has described all admissible linear estimators of the mean vector in a Gauss-Markov model with identity covariance matrix. Further generalizations have been given, among others, by Rao [18], Mathew et al [17], Stępniak [22], Zontek [28], Klonecki and Zontek [12], Baksalary and Markiewicz [1], Baksalary et al [2], Groß and Markiewicz [5] and Stępniak [24]. The problem of characterizing admissible linear estimators of a linear function of expected value was also considered in terms of connection between the closure of the set of unique locally best estimators (ULBE) and the set of admissible linear estimators.…”

Characterization of admissible linear estimators under extended balanced loss function

“…Characterization of admissible linear estimators has received considerable attention in the literature under different models or 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.…”

Admissible invariant estimators in a linear model

“…. , α t are not identifiable by the model (12) in the sense that Ey is not uniquely represented by them. The identifiability may be satisfied by an additional condition, for instance of the form t i=1 α i = 0, called restraint.…”

“…Cohen ( [4,5]), Rao [19] and Stępniak [21] went beyond this classical framework. Further results in this area were given, among others, by LaMotte [14], Klonecki [11], Klonecki and Zontek [12], Baksalary and Markiewicz ( [1,2,3]), Groß and Markiewicz [8] and Stępniak [24]. They were based on the Loewner order of nonnegative definite matrices (see, e. g., Stępniak [22], or Groß ( [6,7])).…”