Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model

Melek Eriş Büyükkaya, (Karadeniz Teknik Üniversitesi, Fen Fakültesi, İstatistik ve Bilgisayar Bilimleri Bölümü, Trabzon, Türkiye)
Nesrin Güler, (Sakarya Üniversitesi, Siyasal Bilgiler Fakültesi, Ekonometri Bölümü, Sakarya, Türkiye)
Melike YİĞİT (Sakarya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Sakarya, Türkiye)
Fundamental journal of mathematics and applications (Online)
1 0
Yıl: 2021 Cilt: 4 Sayı: 3 Sayfa Aralığı: 143 - 149 Metin Dili: İngilizce DOI: 10.33401/fujma.889229 İndeks Tarihi: 29-07-2022

Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model

Öz:
A linear mixed model ($LMM$)$M :yy = mxXBETA+ mxZuu + EPS $ with general assumptions and its transformed model $T:mxTyy = mxTmxXBETA+ mxTmxZuu + mxTEPS $ are considered. This work concerns the comparison problem of predictors under $M$and $T$. Our aim is to establish equality relations between the best linear unbiased predictors ($BLUP$s) of unknown vectors under two $LMM$s $M$and$T$ through their covariance matrices by using various rank formulas of block matrices and elementary matrix operations.
Anahtar Kelime: BLUP linear mixed model covariance matrix transformed model rank

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] C. R. Rao, Representations of best linear unbiased estimators in the Gauss–Markoff model with a singular dispersion matrix, J. Multivariate Anal., 3 (1973), 276-292.
  • [2] B. Dong, W. Guo, Y. Tian, On relations between BLUEs under two transformed linear models, J. Multivariate Anal., 131 (2014), 279-292.
  • [3] Y. Tian, Matrix rank and inertia formulas in the analysis of general linear models, Open Math., 15 (1) (2017), 126-150.
  • [4] G. Marsaglia, G. P. H. Styan, Equalities and inequalities for ranks of matrices, Linear Multilinear Algebra, 2 (1974), 269-292.
  • [5] Y. Tian, Equalities and inequalities for inertias of Hermitian matrices with applications, Linear Algebra Appl., 433 (2010), 263-296.
  • [6] B. Arendack´a, S. Puntanen, Further remarks on the connection between fixed linear model and mixed linear model, Stat. Papers, 56 (4) (2015), 1235-1247.
  • [7] H. Brown, R. Prescott, Applied Mixed Models in Medicine, 2nd edn, Wiley, England, 2006.
  • [8] E. Demidenko, Mixed models: Theory and applications, Wiley, New York, 2004.
  • [9] D. Harville, Extension of the Gauss–Markov theorem to include the estimation of random effects, The Annals of Statistics, 4 (1976), 384-395.
  • [10] S. J. Haslett, S. Puntanen, On the equality of the BLUPs under two linear mixed models, Metrika, 74 (2011), 381-395.
  • [11] S. J. Haslett, S. Puntanen, A review of conditions under which BLUEs and/or BLUPs in one linear mixed model are also BLUEs and/or BLUPs in another, Calcutta Statistical Association Bulletin, 65 (1-4) (2013), 25-42.
  • [12] J. Jiang, Linear and generalized linear mixed models and their applications, Springer, New York, 2007.
  • [13] Y. Liu, On equality of ordinary least squares estimator, best linear unbiased estimator and best linear unbiased predictor in the general linear model, J. Statist. Plann. Inference, 139 (2009), 1522-1529.
  • [14] X. Q. Liu, J. Y. Rong, X. Y. Liu, Best linear unbiased prediction for linear combinations in general mixed linear models, J. Multivariate Anal., 99 (2008), 1503-1517.
  • [15] X. Liu, Q. W. Wang, Equality of the BLUPs under the mixed linear model when random components and errors are correlated, J. Multivariate Anal., 116 (2013), 297-309.
  • [16] G. K. Robinson, That BLUP is a good thing: the estimation of random effects (with discussion on pp. 32-51), Stat. Sci., 6 (1991), 15-51.
  • [17] Y. Tian, A new derivation of BLUPs under random-effects model, Metrika, 78 (2015), 905-918.
  • [18] Y. Tian, B. Jiang, An algebraic study of BLUPs under two linear random-effects models with correlated covariance matrices, Linear Multilinear Algebra, 64 (12) (2016), 2351-2367.
  • [19] Q. W. Wang, X. Liu, The equalities of BLUPs for linear combinations under two general linear mixed models, Commun. Stat.–Theory and Methods, 42 (2013), 3528-3543.
  • [20] J. K. Baksalary, S. Kala, Linear transformations preserving best linear unbiased estimators in a general Gauss–Markoff model, Ann. Stat., 9 (1981), 913-916. [21] N. G¨uler, On relations between BLUPs under two transformed linear random-effects models, Communications in Statistics–Simulation and Computation, (2020), doi:10.1080/03610918.2020.1757709.
  • [22] E. P. Liski, G. Trenkler, J. Grob, Estimation from transformed data under the linear regression model, Statistics, 29 (1997), 205-219.
  • [23] C. H. Morrell, J. D. Pearson, L. J. Brant, Linear transformations of linear mixed-effects models, Am Stat., 51 (1997), 338-343.
  • [24] J. Shao, J. Zhang, A transformation approach in linear mixed-effects models with informative missing responses, Biometrika, 102 (2015), 107-119.
  • [25] Y. Tian, On properties of BLUEs under general linear regression models, J. Statist. Plann. Inference, 143 (2013), 771-782.
  • [26] Y. Tian, Transformation approaches of linear random-effects models, Stat. Methods Appl., 26 (4) (2017), 583-608.
  • [27] Y. Tian, C. Liu, Some equalities for estimations of variance components in a general linear model and its restricted and transformed models, Multivariate Anal., 101 (2010), 1959-1969.
  • [28] Y. Tian, S. Puntanen, On the equivalence of estimations under a general linear model and its transformed models, Linear Algebra Appl., 430 (2009),2622-2641.
  • [29] I. S. Alalouf, G. P. H. Styan, Characterizations of estimability in the general linear model, Ann. Stat., 7 (1979), 194-200.
  • [30] A. S. Goldberger, Best linear unbiased prediction in the generalized linear regression model, J. Amer. Statist. Assoc., 57 (1962), 369-375.
  • [31] S. Puntanen, G. P. H. Styan, J. Isotalo, Matrix Tricks for Linear Statistical Models: Our Personal Top Twenty, Springer, Heidelberg, 2011.
APA ERİŞ BÜYÜKKAYA M, Güler N, YİĞİT M (2021). Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model. , 143 - 149. 10.33401/fujma.889229
Chicago ERİŞ BÜYÜKKAYA Melek,Güler Nesrin,YİĞİT Melike Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model. (2021): 143 - 149. 10.33401/fujma.889229
MLA ERİŞ BÜYÜKKAYA Melek,Güler Nesrin,YİĞİT Melike Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model. , 2021, ss.143 - 149. 10.33401/fujma.889229
AMA ERİŞ BÜYÜKKAYA M,Güler N,YİĞİT M Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model. . 2021; 143 - 149. 10.33401/fujma.889229
Vancouver ERİŞ BÜYÜKKAYA M,Güler N,YİĞİT M Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model. . 2021; 143 - 149. 10.33401/fujma.889229
IEEE ERİŞ BÜYÜKKAYA M,Güler N,YİĞİT M "Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model." , ss.143 - 149, 2021. 10.33401/fujma.889229
ISNAD ERİŞ BÜYÜKKAYA, Melek vd. "Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model". (2021), 143-149. https://doi.org/10.33401/fujma.889229
APA ERİŞ BÜYÜKKAYA M, Güler N, YİĞİT M (2021). Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model. Fundamental journal of mathematics and applications (Online), 4(3), 143 - 149. 10.33401/fujma.889229
Chicago ERİŞ BÜYÜKKAYA Melek,Güler Nesrin,YİĞİT Melike Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model. Fundamental journal of mathematics and applications (Online) 4, no.3 (2021): 143 - 149. 10.33401/fujma.889229
MLA ERİŞ BÜYÜKKAYA Melek,Güler Nesrin,YİĞİT Melike Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model. Fundamental journal of mathematics and applications (Online), vol.4, no.3, 2021, ss.143 - 149. 10.33401/fujma.889229
AMA ERİŞ BÜYÜKKAYA M,Güler N,YİĞİT M Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model. Fundamental journal of mathematics and applications (Online). 2021; 4(3): 143 - 149. 10.33401/fujma.889229
Vancouver ERİŞ BÜYÜKKAYA M,Güler N,YİĞİT M Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model. Fundamental journal of mathematics and applications (Online). 2021; 4(3): 143 - 149. 10.33401/fujma.889229
IEEE ERİŞ BÜYÜKKAYA M,Güler N,YİĞİT M "Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model." Fundamental journal of mathematics and applications (Online), 4, ss.143 - 149, 2021. 10.33401/fujma.889229
ISNAD ERİŞ BÜYÜKKAYA, Melek vd. "Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model". Fundamental journal of mathematics and applications (Online) 4/3 (2021), 143-149. https://doi.org/10.33401/fujma.889229
Sayfa Oluşturulma Tarihi
23-04-2024 21:48

İLETİŞİM

TÜBİTAK ULAKBİM TR Dizin

Yüzüncüyıl, İşçi Blokları Mahallesi

Muhsin Yazıcıoğlu Caddesi No:51/C

06530 Çankaya / ANKARA +90 (312) 298 92 00

trdizin@tubitak.gov.tr

TÜBİTAK ULAKBİM Ulusal Akademik Ağ ve Bilgi Merkezi Cahit Arf Bilgi Merkezi © Tüm Hakları Saklıdır. Gizlilik Politikası Kullanım Şartları