Further remarks on constrained over-parameterized linear models

Nesrin Güler () and Melek Eriş Büyükkaya ()
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Nesrin Güler: Sakarya University
Melek Eriş Büyükkaya: Karadeniz Technical University

Statistical Papers, 2024, vol. 65, issue 2, No 17, 975-988

Abstract: Abstract This paper considers comparison problems for dispersion matrices of predictors under two competing linear models with having the same restrictions on their joint unknown parameters. One of the competing model is a constrained linear model (CLM) and the other one is a constrained over-parameterized model (COLM), obtained by adding new regressors to the CLM. After converting explicitly CLM and its COLM to their implicitly constrained forms, analytical expressions and properties of the best linear unbiased predictors (BLUPs) are given via using some quadratic matrix optimization methods under the models. In particular, the authors provide some equalities and inequalities for dispersion matrices of BLUPs under the models by using some formulas of ranks and inertias of block matrices. Comparison results on the dispersion matrices are also derived for special cases.

Keywords: BLUP; Dispersion matrix; Linear model; Over-parameterized linear model; Restriction (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01426-z

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