Properties of BLUEs and BLUPs in Full vs. Small Linear Models with New Observations

Stephen J. Haslett; Augustyn Markiewicz; Simo Puntanen

doi:10.1007/978-3-030-56773-6_8

Properties of BLUEs and BLUPs in Full vs. Small Linear Models with New Observations

Stephen J. Haslett
, Augustyn Markiewicz
, Simo Puntanen

Computing Sciences

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

3 Citations (Scopus)

58 Downloads (Pure)

Abstract

In this article we consider the partitioned linear model M12={y,X1β1+X2β2,V}, where μ = X1β1 + X2β2, and the corresponding small model M1={y,X1β1,V}, where μ1 = X1β1. These models are supplemented with the new unobservable random vector y∗, coming from y∗ = Kβ1 + ε∗, where the covariance matrix of y∗ is known as well as the cross-covariance matrix between y∗ and y. We focus on comparing the BLUEs of μ1 and μ, and BLUPs of y∗ and ε∗ under M12 and M1.

Original language	English
Title of host publication	Recent Developments in Multivariate and Random Matrix Analysis
Subtitle of host publication	Festschrift in Honour of Dietrich von Rosen
Editors	Thomas Holgersson, Martin Singull
Publisher	Springer
Chapter	8
Pages	123-146
Number of pages	24
ISBN (Electronic)	978-3-030-56773-6
ISBN (Print)	978-3-030-56772-9
DOIs	https://doi.org/10.1007/978-3-030-56773-6_8
Publication status	Published - 2020
Publication type	A3 Book chapter

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10.1007/978-3-030-56773-6_8

HasMarPun-DVR65-2020
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http://urn.fi/URN:NBN:fi:tuni-202102021864

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abstract = "In this article we consider the partitioned linear model M12=\{y,X1β1+X2β2,V\}, where μ = X1β1 + X2β2, and the corresponding small model M1=\{y,X1β1,V\}, where μ1 = X1β1. These models are supplemented with the new unobservable random vector y∗, coming from y∗ = Kβ1 + ε∗, where the covariance matrix of y∗ is known as well as the cross-covariance matrix between y∗ and y. We focus on comparing the BLUEs of μ1 and μ, and BLUPs of y∗ and ε∗ under M12 and M1.",

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doi = "10.1007/978-3-030-56773-6\_8",

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Properties of BLUEs and BLUPs in Full vs. Small Linear Models with New Observations. / Haslett, Stephen J.; Markiewicz, Augustyn; Puntanen, Simo.
Recent Developments in Multivariate and Random Matrix Analysis: Festschrift in Honour of Dietrich von Rosen. ed. / Thomas Holgersson; Martin Singull. Springer, 2020. p. 123-146.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

TY - CHAP

T1 - Properties of BLUEs and BLUPs in Full vs. Small Linear Models with New Observations

AU - Haslett, Stephen J.

AU - Markiewicz, Augustyn

AU - Puntanen, Simo

PY - 2020

Y1 - 2020

N2 - In this article we consider the partitioned linear model M12={y,X1β1+X2β2,V}, where μ = X1β1 + X2β2, and the corresponding small model M1={y,X1β1,V}, where μ1 = X1β1. These models are supplemented with the new unobservable random vector y∗, coming from y∗ = Kβ1 + ε∗, where the covariance matrix of y∗ is known as well as the cross-covariance matrix between y∗ and y. We focus on comparing the BLUEs of μ1 and μ, and BLUPs of y∗ and ε∗ under M12 and M1.

AB - In this article we consider the partitioned linear model M12={y,X1β1+X2β2,V}, where μ = X1β1 + X2β2, and the corresponding small model M1={y,X1β1,V}, where μ1 = X1β1. These models are supplemented with the new unobservable random vector y∗, coming from y∗ = Kβ1 + ε∗, where the covariance matrix of y∗ is known as well as the cross-covariance matrix between y∗ and y. We focus on comparing the BLUEs of μ1 and μ, and BLUPs of y∗ and ε∗ under M12 and M1.

U2 - 10.1007/978-3-030-56773-6_8

DO - 10.1007/978-3-030-56773-6_8

M3 - Chapter

SN - 978-3-030-56772-9

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EP - 146

BT - Recent Developments in Multivariate and Random Matrix Analysis

A2 - Holgersson, Thomas

A2 - Singull, Martin

PB - Springer

ER -

Properties of BLUEs and BLUPs in Full vs. Small Linear Models with New Observations

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