On comparison of dispersion matrices of estimators under a constrained linear model

Yongge Tian () and Wenxing Guo ()
Additional contact information
Wenxing Guo: Central University of Finance and Economics

Statistical Methods & Applications, 2016, vol. 25, issue 4, No 6, 623-649

Abstract: Abstract We introduce some new mathematical tools in the analysis of dispersion matrices of the two well-known OLSEs and BLUEs under general linear models with parameter restrictions. We first establish some formulas for calculating the ranks and inertias of the differences of OLSEs’ and BLUEs’ dispersion matrices of parametric functions under the general linear model $${\mathscr {M}}= \{\mathbf{y}, \ \mathbf{X }\pmb {\beta }, \ \pmb {\Sigma }\}$$ M = { y , X β , Σ } and the constrained model $${\mathscr {M}}_r = \{\mathbf{y}, \, \mathbf{X }\pmb {\beta }\, | \, \mathbf{A }\pmb {\beta }= \mathbf{b}, \ \pmb {\Sigma }\}$$ M r = { y , X β | A β = b , Σ } , where $$\mathbf{A }\pmb {\beta }= \mathbf{b}$$ A β = b is a consistent linear matrix equation for the unknown parameter vector $$\pmb {\beta }$$ β to satisfy. As applications, we derive necessary and sufficient conditions for many equalities and inequalities of OLSEs’ and BLUEs’ dispersion matrices to hold under $${\mathscr {M}}$$ M and $${\mathscr {M}}_r$$ M r .

Keywords: Constrained linear model; OLSE; BLUE; Dispersion matrix; Rank; Inertia; Equality; Inequality; 15A09; 62J05; 62H12 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10260-016-0350-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stmapp:v:25:y:2016:i:4:d:10.1007_s10260-016-0350-2

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10260/PS2

DOI: 10.1007/s10260-016-0350-2

Access Statistics for this article

Statistical Methods & Applications is currently edited by Tommaso Proietti

More articles in Statistical Methods & Applications from Springer, Società Italiana di Statistica
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().