Some Remarks on Comparison of Predictors in Seemingly Unrelated Linear Mixed Models

Guler N., Buyukkaya M. E.

APPLICATIONS OF MATHEMATICS, cilt.67, sa.4, ss.525-542, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 67 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.21136/am.2021.0366-20
  • Dergi Adı: APPLICATIONS OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Compendex, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.525-542
  • Anahtar Kelimeler: BLUP, covariance matrix, inertia, OLSP, rank, SULMM, SURM, UNBIASED PREDICTION, REGRESSIONS, ESTIMATORS, MATRICES, FORMULAS
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we consider a comparison problem of predictors in the context of linear mixed models. In particular, we assume a set of m different seemingly unrelated linear mixed models (SULMMs) allowing correlations among random vectors across the models. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of joint unknown vectors under SULMMs and their combined model. We use the matrix rank and inertia method for establishing equalities and inequalities. We also give an extensive approach for seemingly unrelated regression models (SURMs) by applying the results obtained for SULMMs to SURMs.