Some Remarks on the Equalities of Predictors in Linear Mixed Models

Melike YİĞİT, (Sakarya Üniversitesi, Matematik Bölümü, 54187, Sakarya, Türkiye)
Nesrin GÜLER, (Sakarya Üniversitesi, Ekonometri Bölümü, 54187, Sakarya, Türkiye)
Melek ERİŞ BÜYÜKKAYA (Karadeniz Teknik Üniversitesi, İstatistik ve Bilgisayar Bilimleri Bölümü, 61080, Trabzon, Türkiye)
Mathematical Sciences and Applications E-Notes
0 0
Yıl: 2021 Cilt: 9 Sayı: 4 Sayfa Aralığı: 185 - 193 Metin Dili: İngilizce DOI: 10.36753/mathenot.892258 İndeks Tarihi: 16-07-2023

Some Remarks on the Equalities of Predictors in Linear Mixed Models

Öz:
Consider a transformed linear mixed model (TLMM) obtained pre-multiplying a linear mixed model (LMM) M : y = Zα + Rγ + e by a given matrix. This work concerns the problem of the equalities of linear predictors under the considered two LMMs under general assumptions. We characterize the equalities between the best linear unbiased predictors (BLUPs) under the LMM and its TLMM by using various rank formulas of block matrices and elementary matrix operations.
Anahtar Kelime: BLUP equalities linear mixed model random vectors transformed model

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Alalouf, I. S., Styan, G. P. H.: Characterizations of estimability in the general linear model. Ann. Stat. 7, 194-200 (1979).
  • [2] Arendacká, B., Puntanen, S.: Further remarks on the connection between fixed linear model and mixed linear model. Stat. Papers. 56 (4), 1235-1247 (2015).
  • [3] Baksalary, J. K., Kala, S.: Linear transformations preserving best linear unbiased estimators in a general Gauss-Markoff model. Ann. Stat. 9, 913-916 (1981).
  • [4] Dong, B., Guo, W., Tian, Y.: On relations between BLUEs under two transformed linear models. J. Multivariate Anal. 131, 279-292 (2014).
  • [5] Drygas, H.: Sufficiency and completeness in the general Gauss-Markov model. Sankhya ̄, Ser A. 45, 88-98 (1983).
  • [6] Goldberger, A. S.: Best linear unbiased prediction in the generalized linear regression model. J. Amer. Statist. Assoc. 57, 369-375 (1962).
  • [7] Güler, N.: On relations between BLUPs under two transformed linear random-effects models. Commun. Statist. Simulation and Computation. (2020). https://doi.org/10.1080/03610918.2020.1757709
  • [8] Harville, D.: Extension of the Gauss-Markov theorem to include the estimation of random effects. Ann. Stat. 4, 384-395 (1976).
  • [9] Haslett, S. J., Puntanen, S.: Equality of BLUEs or BLUPs under two linear models using stochastic restrictions. Stat. Papers. 51 (2), 465-475 (2010).
  • [10] Haslett, S. J., Puntanen, S.: On the equality of the BLUPs under two linear mixed models. Metrika. 74, 381-395 (2011).
  • [11] Isotalo, J., Puntanen, S.: Linear prediction sufficiency for new observations in the general Gauss–Markov model. Commun. Statist. Theory and Methods. 35, 1011-1023 (2006).
  • [12] Liu, X., Wang, Q. W.: Equality of the BLUPs under the mixed linear model when random components and errors are correlated. J. Multivariate Anal. 116, 297-309 (2013).
  • [13] Marsaglia, G., Styan, G. P. H.: Equalities and inequalities for ranks of matrices, Linear Multilinear Algebra. 2, 269-292 (1974).
  • [14] Penrose, R.: Generalized inverse for matrices. Proc. Cambridge Philos. Soc. 51, 406-413 (1955).
  • [15] Puntanen, S., Styan, G. P. H. , Isotalo, J.: Matrix Tricks for Linear Statistical Models: Our Personal Top Twenty. Springer, Heidelberg (2011).
  • [16] Rao, C. R.: Representations of best linear unbiased estimators in the Gauss–Markoff model with a singular dispersion matrix. J. Multivariate Anal. 3, 276-292 (1973).
  • [17] Sun, Y., Jiang B., Jiang, H.: Computations of predictors/estimators under a linear random–effects model with parameter restrictions. Commun. Statist. Theory and Methods. 48 (14), 3482-3497 (2019).
  • [18] Tian, Y.: The maximal and minimal ranks of some expressions of generalized inverses of matrices. Southeast Asian Bull. Math. 25, 745-755 (2002).
  • [19] Tian, Y.: On equalities for BLUEs under misspecified Gauss-Markov models. Acta Mathematica Sinica. Eng. Ser. 25 (11), 1907-1920 (2009).
  • [20] Tian, Y.: A new derivation of BLUPs under random-effects model. Metrika. 78, 905-918 (2015).
  • [21] Tian, Y.: A matrix handling of predictions under a general linear random-effects model with new observations. Electron. J. Linear Algebra. 29, 30-45 (2015).
  • [22] Tian, Y.: Transformation approaches of linear random-effects models. Stat. Methods Appl. 26 (4), 583-608 (2017).
  • [23] Tian, Y., Cheng, S.: The maximal and minimal ranks of A-BXC with applications. New York J. Math. 9, 345-362 (2003).
  • [24] Tian, Y., Puntanen, S.: On the equivalence of estimations under a general linear model and its transformed models. Linear Algebra Appl. 430, 2622-2641 (2009).
  • [25] Tian, Y., Jiang, B.: An algebraic study of BLUPs under two linear random-effects models with correlated covariance matrices. Linear Multilinear Algebra. 64 (12), 2351-2367 (2016).
  • [26] Tian, Y., Jiang B.: Matrix rank/inertia formulas for least-squares solutions with statistical applications. Spec. Matrices. 4 (1), 130-140 (2016).
APA YİĞİT M, Güler N, ERİŞ BÜYÜKKAYA M (2021). Some Remarks on the Equalities of Predictors in Linear Mixed Models. , 185 - 193. 10.36753/mathenot.892258
Chicago YİĞİT Melike,Güler Nesrin,ERİŞ BÜYÜKKAYA Melek Some Remarks on the Equalities of Predictors in Linear Mixed Models. (2021): 185 - 193. 10.36753/mathenot.892258
MLA YİĞİT Melike,Güler Nesrin,ERİŞ BÜYÜKKAYA Melek Some Remarks on the Equalities of Predictors in Linear Mixed Models. , 2021, ss.185 - 193. 10.36753/mathenot.892258
AMA YİĞİT M,Güler N,ERİŞ BÜYÜKKAYA M Some Remarks on the Equalities of Predictors in Linear Mixed Models. . 2021; 185 - 193. 10.36753/mathenot.892258
Vancouver YİĞİT M,Güler N,ERİŞ BÜYÜKKAYA M Some Remarks on the Equalities of Predictors in Linear Mixed Models. . 2021; 185 - 193. 10.36753/mathenot.892258
IEEE YİĞİT M,Güler N,ERİŞ BÜYÜKKAYA M "Some Remarks on the Equalities of Predictors in Linear Mixed Models." , ss.185 - 193, 2021. 10.36753/mathenot.892258
ISNAD YİĞİT, Melike vd. "Some Remarks on the Equalities of Predictors in Linear Mixed Models". (2021), 185-193. https://doi.org/10.36753/mathenot.892258
APA YİĞİT M, Güler N, ERİŞ BÜYÜKKAYA M (2021). Some Remarks on the Equalities of Predictors in Linear Mixed Models. Mathematical Sciences and Applications E-Notes, 9(4), 185 - 193. 10.36753/mathenot.892258
Chicago YİĞİT Melike,Güler Nesrin,ERİŞ BÜYÜKKAYA Melek Some Remarks on the Equalities of Predictors in Linear Mixed Models. Mathematical Sciences and Applications E-Notes 9, no.4 (2021): 185 - 193. 10.36753/mathenot.892258
MLA YİĞİT Melike,Güler Nesrin,ERİŞ BÜYÜKKAYA Melek Some Remarks on the Equalities of Predictors in Linear Mixed Models. Mathematical Sciences and Applications E-Notes, vol.9, no.4, 2021, ss.185 - 193. 10.36753/mathenot.892258
AMA YİĞİT M,Güler N,ERİŞ BÜYÜKKAYA M Some Remarks on the Equalities of Predictors in Linear Mixed Models. Mathematical Sciences and Applications E-Notes. 2021; 9(4): 185 - 193. 10.36753/mathenot.892258
Vancouver YİĞİT M,Güler N,ERİŞ BÜYÜKKAYA M Some Remarks on the Equalities of Predictors in Linear Mixed Models. Mathematical Sciences and Applications E-Notes. 2021; 9(4): 185 - 193. 10.36753/mathenot.892258
IEEE YİĞİT M,Güler N,ERİŞ BÜYÜKKAYA M "Some Remarks on the Equalities of Predictors in Linear Mixed Models." Mathematical Sciences and Applications E-Notes, 9, ss.185 - 193, 2021. 10.36753/mathenot.892258
ISNAD YİĞİT, Melike vd. "Some Remarks on the Equalities of Predictors in Linear Mixed Models". Mathematical Sciences and Applications E-Notes 9/4 (2021), 185-193. https://doi.org/10.36753/mathenot.892258
Sayfa Oluşturulma Tarihi
24-04-2024 8:23

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