Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model
Fundamental journal of mathematics and applications (Online), cilt.4, sa.3, ss.143-149, 2021 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 4 Sayı: 3
- Basım Tarihi: 2021
- Doi Numarası: 10.33401/fujma.889229
- Dergi Adı: Fundamental journal of mathematics and applications (Online)
- Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.143-149
- Karadeniz Teknik Üniversitesi Adresli: Evet
Özet
A linear mixed model (\LMM " role="presentation" >\LMM) \M : \yy = \mxX \BETA + \mxZ \uu + \EPS " role="presentation" >\M:\yy=\mxX\BETA+\mxZ\uu+\EPS with general assumptions and its transformed model \T : \mxT \yy = \mxT \mxX \BETA + \mxT \mxZ \uu + \mxT \EPS " role="presentation" >\T:\mxT\yy=\mxT\mxX\BETA+\mxT\mxZ\uu+\mxT\EPS are considered. This work concerns the comparison problem of predictors under \M " role="presentation" >\M and \T " role="presentation" >\T. Our aim is to establish equality relations between the best linear unbiased predictors (\BLUP " role="presentation" >\BLUPs) of unknown vectors under two \LMM " role="presentation" >\LMMs \M " role="presentation" >\M and \T " role="presentation" >\T through their covariance matrices by using various rank formulas of block matrices and elementary matrix operations.