Equivalence of predictors under real and over-parameterized linear models

Shengjun Gan, Yuqin Sun and Yongge Tian

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 11, 5368-5383

Abstract: Assume that a real linear model y=Xβ+ε${\bf y}= {\bf X}\pmb {\beta }+ \pmb {\varepsilon }$ is over-parameterized as y=Xβ+Zγ+ε${\bf y}= {\bf X}\pmb {\beta }+ {\bf Z}\pmb {\gamma }+ \pmb {\varepsilon }$ by adding some new regressors Zγ${\bf Z}\pmb {\gamma }$. In such a case, results of statistical inferences of the unknown parameters β$\pmb {\beta }$ and ε$\pmb {\varepsilon }$ under the two models are not necessarily the same. This paper aims at characterizing relationships between the best linear unbiased predictors (BLUPs) of the joint vector ϕ=Kβ+Jε$\pmb {\phi }= {\bf K}\pmb {\beta }+ {\bf J}\pmb {\varepsilon }$ of the unknown parameters in the two models. In particular, we derive necessary and sufficient conditions for the BLUPs of ϕ$\pmb {\phi }$ to be equivalent under the real model and its over-parameterized counterpart.

Date: 2017
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2015.1100742 (text/html)
Access to full text is restricted to subscribers.

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:taf:lstaxx:v:46:y:2017:i:11:p:5368-5383

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2015.1100742

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().