Comparison of predictors under constrained general linear model and its future observations

Eriş Büyükkaya M.

COMMUNICATIONS IN STATISTICS -THEORY AND METHODS, cilt.53, sa.24, ss.8929-8941, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 24
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1080/03610926.2024.2314618
  • Dergi Adı: COMMUNICATIONS IN STATISTICS -THEORY AND METHODS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Business Source Elite, Business Source Premier, CAB Abstracts, Compendex, Computer & Applied Sciences, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.8929-8941
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

This study deals with some basic inference problems about future observations in a general linear model (GLM) with linear parameter constraints, known as a constrained general linear model (CGLM). Combining the CGLM and its future observations, the author turns the model into a reparameterized form. Using some quadratic matrix optimization methods, the author derives analytical formulas for calculating the best linear unbiased predictors (BLUPs) of all unknown parameter matrices under a CGLM and its future observations. In particular, the author next gives a comprehensive search on the comparison of dispersion matrices of BLUPs of unknown vectors by establishing various equalities and inequalities for dispersion matrices of BLUPs under the model by using elementary block matrix operations and some formulas of rank and inertia of block matrices.