Admissible invariant estimators in a linear model

Title:

Admissible invariant estimators in a linear model

Creator:

Stępniak, Czesław

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8af88523-b931-4e9a-8a82-7e722be90a1d
uuid:8af88523-b931-4e9a-8a82-7e722be90a1d

Subject:

linear estimator, invariant estimator, admissibility, and one-way / two-way ANOVA

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let y be observation vector in the usual linear model with expectation Aβ and covariance matrix known up to a multiplicative scalar, possibly singular. A linear statistic aTy is called invariant estimator for a parametric function ϕ=cTβ if its MSE depends on β only through ϕ. It is shown that aTy is admissible invariant for ϕ, if and only if, it is a BLUE of ϕ, in the case when ϕ is estimable with zero variance, and it is of the form kϕˆ, where k∈⟨0,1⟩ and ϕˆ is an arbitrary BLUE, otherwise. This result is used in the one- and two-way ANOVA models. Our paper is self-contained and accessible, also for non-specialists.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[310]-321

Source:

Kybernetika | 2014 Volume:50 | Number:3

Harvested from:

CDK

Metadata only:

false