Properties of BLUEs in full versus small linear models

Stephen J. Haslett; Augustyn Markiewicz; Simo Puntanen

doi:10.1080/03610926.2022.2052899

Properties of BLUEs in full versus small linear models

Stephen J. Haslett, Augustyn Markiewicz, Simo Puntanen

Computing Sciences

Research output: Contribution to journal › Article › Scientific › peer-review

2 Citations (Scopus)

4 Downloads (Pure)

Abstract

In this article we consider the partitioned linear model M12={y, X1β1+X2β2, V} and the corresponding small model M1={y, X1β1, V}. We focus on comparing the best linear unbiased estimators, BLUEs, of X1β1 under M12 and M1. In other words, we are interested in the effect of adding regressors on the BLUEs. Particular attention is paid on the consistency of the model, that is, whether the realized value of the response vector y belongs to the column space of (X1:V) or (X1:X2:V).

Original language	English
Pages (from-to)	7684-7698
Number of pages	15
Journal	Communications in Statistics - Theory and Methods
Volume	52
Issue number	21
Early online date	29 Mar 2022
DOIs	https://doi.org/10.1080/03610926.2022.2052899
Publication status	Published - 2023
Publication type	A1 Journal article-refereed

Keywords

Best linear unbiased estimator; BLUE; Lowner ordering; partitioned linear model; adding regressors

Publication forum classification

Publication forum level 1

Access to Document

10.1080/03610926.2022.2052899Licence: CC BY-NC-ND

03610926.2022Final published version, 1.09 MBLicence: CC BY-NC-ND

https://urn.fi/URN:NBN:fi:tuni-202204263619Licence: CC BY-NC-ND

Cite this

@article{5b119a4578bb4217bf0a8facfc35f2e0,

title = "Properties of BLUEs in full versus small linear models",

abstract = "In this article we consider the partitioned linear model M12={y, X1β1+X2β2, V} and the corresponding small model M1={y, X1β1, V}. We focus on comparing the best linear unbiased estimators, BLUEs, of X1β1 under M12 and M1. In other words, we are interested in the effect of adding regressors on the BLUEs. Particular attention is paid on the consistency of the model, that is, whether the realized value of the response vector y belongs to the column space of (X1:V) or (X1:X2:V).",

keywords = "Best linear unbiased estimator; BLUE; Lowner ordering; partitioned linear model; adding regressors",

author = "Haslett, {Stephen J.} and Augustyn Markiewicz and Simo Puntanen",

year = "2023",

doi = "10.1080/03610926.2022.2052899",

language = "English",

volume = "52",

pages = "7684--7698",

number = "21",

}

TY - JOUR

T1 - Properties of BLUEs in full versus small linear models

AU - Haslett, Stephen J.

AU - Markiewicz, Augustyn

AU - Puntanen, Simo

PY - 2023

Y1 - 2023

N2 - In this article we consider the partitioned linear model M12={y, X1β1+X2β2, V} and the corresponding small model M1={y, X1β1, V}. We focus on comparing the best linear unbiased estimators, BLUEs, of X1β1 under M12 and M1. In other words, we are interested in the effect of adding regressors on the BLUEs. Particular attention is paid on the consistency of the model, that is, whether the realized value of the response vector y belongs to the column space of (X1:V) or (X1:X2:V).

AB - In this article we consider the partitioned linear model M12={y, X1β1+X2β2, V} and the corresponding small model M1={y, X1β1, V}. We focus on comparing the best linear unbiased estimators, BLUEs, of X1β1 under M12 and M1. In other words, we are interested in the effect of adding regressors on the BLUEs. Particular attention is paid on the consistency of the model, that is, whether the realized value of the response vector y belongs to the column space of (X1:V) or (X1:X2:V).

KW - Best linear unbiased estimator; BLUE; Lowner ordering; partitioned linear model; adding regressors

U2 - 10.1080/03610926.2022.2052899

DO - 10.1080/03610926.2022.2052899

M3 - Article

SN - 0361-0926

VL - 52

SP - 7684

EP - 7698

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 21

ER -

Properties of BLUEs in full versus small linear models

Abstract

Keywords

Publication forum classification

Access to Document

Fingerprint

Cite this