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

Stephen J. Haslett (), Augustyn Markiewicz () and Simo Puntanen ()
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Stephen J. Haslett: Massey University, School of Fundamental Sciences
Augustyn Markiewicz: Poznań University of Life Sciences, Department of Mathematical and Statistical Methods
Simo Puntanen: Tampere University, Faculty of Information Technology and Communication Sciences

Chapter Chapter 8 in Recent Developments in Multivariate and Random Matrix Analysis, 2020, pp 123-146 from Springer

Abstract: Abstract In this article we consider the partitioned linear model M 12 = { y , X 1 β 1 + X 2 β 2 , V } $$ \mathcal {M}_{12} = \{ \mathbf {y}, \, {\mathbf {X}}_{1}\boldsymbol {\beta }_{1} + {\mathbf {X}}_{2}\boldsymbol {\beta }_{2}, \, \mathbf {V} \}$$ , where μ = X 1β 1 + X 2β 2, and the corresponding small model M 1 = { y , X 1 β 1 , V } $$ \mathcal {M}_{1} = \{ \mathbf {y}, \, {\mathbf {X}}_{1} \boldsymbol {\beta }_{1}, \, \mathbf {V} \}$$ , where μ 1 = X 1β 1. These models are supplemented with the new unobservable random vector y ∗, coming from y ∗ = Kβ 1 + 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 μ 1 and μ, and BLUPs of y ∗ and ε ∗ under M 12 $$ \mathcal {M}_{12} $$ and M 1 $$\mathcal {M}_{1}$$ .

Date: 2020
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DOI: 10.1007/978-3-030-56773-6_8

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