A matrix approach to determine optimal predictors in a constrained linear mixed model

Guler N., ERİŞ BÜYÜKKAYA M.

OPEN MATHEMATICS, cilt.22, sa.1, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1515/math-2024-0114
  • Dergi Adı: OPEN MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

For a general vector of all unknown vectors in a constrained linear mixed model (CLMM), this study compared the dispersion matrices of the best linear unbiased predictors with any symmetric matrix for determining the optimality of predictors among others. Using the methodology of block matrix inertias and ranks as well as elementary block matrix operations, some equalities and inequalities are derived for comparisons. Additionally, the comparison findings for the CLMM reduce to special instances of the general vector of all unknown vectors. We also provide some comparison findings between the CLMM and its unconstrained form. Finally, we give a numerical example to illustrate our theoretical findings.