A complete class for linear estimation in a general linear model

Abstract

SummaryIt is shown that in linear estimation, both unbiased and biased, all unique (up to equivalence with respect to risk) locally best estimators and their limits constitute a complete class.

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

“…Note that using Theorem 2.2 we get all admissible linear estimators of K EY among L. This is due to the fact that every ULBE is admissible among L (see LaMotte [12]) and that all ULBE's and their limits constitute a complete class (see Stȩpniak [21] and LaMotte [13]). …”

“…The first set contains the second one. Using Bayes DOI: 10.14736/kyb-2016-5-0724 approach this was proved by Stȩpniak [21] but his proof was not constructive. LaMotte [13] presented a construction of a sequence of unique locally best linear estimators that converged to the given admissible linear estimator.…”

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

“…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. This approach was applied, among others, by Stępniak [23], Zontek [29] and LaMotte [15]. LaMotte has shown that every admisible linear estimator is the limit of linear estimators that are uniquely best at points in the minimal closed convex cone containing the original parameter set.…”

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.…”