# On decompositions of estimators under a general linear model with partial parameter restrictions

Open Mathematics (2017)

• Volume: 15, Issue: 1, page 1300-1322
• ISSN: 2391-5455

top

## Abstract

top
A general linear model can be given in certain multiple partitioned forms, and there exist submodels associated with the given full model. In this situation, we can make statistical inferences from the full model and submodels, respectively. It has been realized that there do exist links between inference results obtained from the full model and its submodels, and thus it would be of interest to establish certain links among estimators of parameter spaces under these models. In this approach the methodology of additive matrix decompositions plays an important role to obtain satisfactory conclusions. In this paper, we consider the problem of establishing additive decompositions of estimators in the context of a general linear model with partial parameter restrictions. We will demonstrate how to decompose best linear unbiased estimators (BLUEs) under the constrained general linear model (CGLM) as the sums of estimators under submodels with parameter restrictions by using a variety of effective tools in matrix analysis. The derivation of our main results is based on heavy algebraic operations of the given matrices and their generalized inverses in the CGLM, while the whole contributions illustrate various skillful uses of state-of-the-art matrix analysis techniques in the statistical inference of linear regression models.

## How to cite

top

Bo Jiang, Yongge Tian, and Xuan Zhang. "On decompositions of estimators under a general linear model with partial parameter restrictions." Open Mathematics 15.1 (2017): 1300-1322. <http://eudml.org/doc/288393>.

@article{BoJiang2017,
abstract = {A general linear model can be given in certain multiple partitioned forms, and there exist submodels associated with the given full model. In this situation, we can make statistical inferences from the full model and submodels, respectively. It has been realized that there do exist links between inference results obtained from the full model and its submodels, and thus it would be of interest to establish certain links among estimators of parameter spaces under these models. In this approach the methodology of additive matrix decompositions plays an important role to obtain satisfactory conclusions. In this paper, we consider the problem of establishing additive decompositions of estimators in the context of a general linear model with partial parameter restrictions. We will demonstrate how to decompose best linear unbiased estimators (BLUEs) under the constrained general linear model (CGLM) as the sums of estimators under submodels with parameter restrictions by using a variety of effective tools in matrix analysis. The derivation of our main results is based on heavy algebraic operations of the given matrices and their generalized inverses in the CGLM, while the whole contributions illustrate various skillful uses of state-of-the-art matrix analysis techniques in the statistical inference of linear regression models.},
author = {Bo Jiang, Yongge Tian, Xuan Zhang},
journal = {Open Mathematics},
keywords = {Partitioned linear model; Submodel; Parameter restriction; BLUE; Additive matrix decomposition},
language = {eng},
number = {1},
pages = {1300-1322},
title = {On decompositions of estimators under a general linear model with partial parameter restrictions},
url = {http://eudml.org/doc/288393},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Bo Jiang
AU - Yongge Tian
AU - Xuan Zhang
TI - On decompositions of estimators under a general linear model with partial parameter restrictions
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 1300
EP - 1322
AB - A general linear model can be given in certain multiple partitioned forms, and there exist submodels associated with the given full model. In this situation, we can make statistical inferences from the full model and submodels, respectively. It has been realized that there do exist links between inference results obtained from the full model and its submodels, and thus it would be of interest to establish certain links among estimators of parameter spaces under these models. In this approach the methodology of additive matrix decompositions plays an important role to obtain satisfactory conclusions. In this paper, we consider the problem of establishing additive decompositions of estimators in the context of a general linear model with partial parameter restrictions. We will demonstrate how to decompose best linear unbiased estimators (BLUEs) under the constrained general linear model (CGLM) as the sums of estimators under submodels with parameter restrictions by using a variety of effective tools in matrix analysis. The derivation of our main results is based on heavy algebraic operations of the given matrices and their generalized inverses in the CGLM, while the whole contributions illustrate various skillful uses of state-of-the-art matrix analysis techniques in the statistical inference of linear regression models.
LA - eng
KW - Partitioned linear model; Submodel; Parameter restriction; BLUE; Additive matrix decomposition
UR - http://eudml.org/doc/288393
ER -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.