A characterization of admissible linear estimators of fixed and random effects in linear models

Abstract

Linear model, Linear estimation, Linear prediction, Admissibility, Admissibility among an affine set, Locally best estimator,

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

“…Note that Y has an multivariate normal distribution with the following parameters (10) reduces to so the called one-way balanced random model. Following Synówka-Bejenka and Zontek [23], to obtain explicit formulas for ULBE in model (8) corresponding to model (10), we define the following matrices…”

“…Using the rule of duality, Synówka-Bejenka and Zontek [23] obtained a characterization of linear admissible estimators of a linear function of fixed and random effects in the k-way balanced nested classification random model and the k-way balanced crossed classification random model. To prove that in the considered models each limit of ULBE's is admissible, they applied a step-wise procedure of LaMotte [12].…”

“…To give a characterization of linear admissible estimators of θ, Synówka-Bejenka and Zontek [23] reduced the problem to linear estimation of the fixed effects only in another properly defined dual model. We briefly recall this result.…”

“…Synówka-Bejenka and Zontek [23] have shown that a problem of admissibility for a linear function of fixed and random effects could be restarted as a problem of admissibility for a linear function of the expected value only, in another properly defined linear model (called the dual model). Basing on LaMotte's results [12,13] they have given in an explicit form a characterization of linear admissible estimators of a linear function of expected value in the models dual to balanced nested and crossed classification random models (see also Shiqing et al [19]).…”

Admissible invariant estimators in a linear model

“…Subsequent works by Stępniak [23], Zontek [29], LaMotte [15] and Synówka-Bejenka and Zontek [28] introduced a new tool in the problem of admissibility. It is based on the DOI: 10.14736/kyb-2014- limits of the unique locally best linear estimators.…”