Admissible linear estimation in the general Gauss-Markov model with respect to an arbitrary quadratic risk function

Baksalary, Jerzy K. ; Markiewiczb, Augustyn ; Radhakrishna Rao, C. (1995) Admissible linear estimation in the general Gauss-Markov model with respect to an arbitrary quadratic risk function Journal of Statistical Planning and Inference, 44 (3). pp. 341-347. ISSN 0378-3758

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/037837...

Related URL: http://dx.doi.org/10.1016/0378-3758(94)00081-6

Abstract

In the first part of this paper, we give a complete characterization of the class, AW(Kβ) of all estimators that are admissible for any given vector of parametric functions Kβ, not necessarily identifiable, among the set of linear estimators under the general Gauss-Markov model M = {Y, Xβ, σ2V}, with both the model matrix X and the dispersion matrix V possibly deficient in rank, when the criterion for comparing estimators is the W-weighted quadratic risk function, with any nonnegative definite weight-matrix W. In the second part, we investigate the robustness of the class AW(Kβ) with respect to W, with the conclusion that, except for special situations only, there is full freedom in choosing W within the set of matrices having the same range.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:General Gauss-Markov Model; Singular Linear Model; Linear Estimator; Admissiblity; Quadratic Risk Function; Identifiable Parametric Function; Unidentifiable Parametric Function
ID Code:42477
Deposited On:04 Jun 2011 08:48
Last Modified:04 Jun 2011 08:48

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