Araştırma Makalesi
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Yıl 2022, Cilt: 5 Sayı: 3, 192 - 200, 23.09.2022

Melek Eriş Büyükkaya Nesrin Güler

https://doi.org/10.33401/fujma.1134600
Cited By: 1

Öz

Kaynakça

  • [1] P. Bhimasankaram, R. SahaRay, On a partitioned linear model and some associated reduced models, Linear Algebra Appl., 264 (1997), 329–339.
  • [2] J. Grob, S. Puntanen, Estimation under a general partitioned linear model, Linear Algebra Appl., 321 (2000), 131–144.
  • [3] 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.
  • [4] J. K. Baksalary, P. R. Pordzik, Implied linear restrictions in the general Gauss–Markov model, J. Statist. Plann. Inference, 30 (1992), 237–248.
  • [5] A. R. Gallant, T. M. Gerig, Computations for constrained linear models, Econometrics, 12 (1) (1980), 59–84.
  • [6] S. J. Haslett, S. Puntanen, Equality of BLUEs or BLUPs under two linear models using stochastic restrictions, Stat. Papers, 51 (2010), 465–475.
  • [7] H. Jiang, J. Qian, Y. Sun, Best linear unbiased predictors and estimators under a pair of constrained seemingly unrelated regression models, Stat. Probab. Lett., 158 (2020), 108669.
  • [8] B. Jiang, Y. Sun, On the equality of estimators under a general partitioned linear model with parameter restrictions, Stat. Papers, 60 (2019), 273–292.
  • [9] B. Jiang, Y. Tian, Decomposition approaches of a constrained general linear model with fixed parameters, Electron. J. Linear Algebra, 32 (2017), 232–253.
  • [10] B. Jiang, Y. Tian, X. Zhang, On decompositions of estimators under a general linear model with partial parameter restrictions, Open Math., 15 (2017), 1300–1322.
  • [11] M. Liu, Y. Tian, R. Yuan, Statistical inference of a partitioned linear random-effects model, Commun. Statist. Theory Methods, (2021), doi: 10.1080/03610926.2021.1926509.
  • [12] R. Ma, Y. Tian, A matrix approach to a general partitioned linear model with partial parameter restrictions, Linear Multilinear Algebra, (2020), doi: 10.1080/03081087.2020.1804521.
  • [13] Y. Tian, On equalities of estimations of parametric functions under a general linear model and its restricted models, Metrika, 72 (3) (2010b), 313–330.
  • [14] Y. Tian, W. Guo, On comparison of dispersion matrices of estimators under a constrained linear model, Stat. Methods Appl., 25 (4) (2016), 623–649.
  • [15] Y. Tian, B. Jiang, Equalities for estimators of partial parameters under linear model with restrictions, J. Multivariate Anal., 143 (2016), 299–313.
  • [16] Y. Tian, J. Wang, Some remarks on fundamental formulas and facts in the statistical analysis of a constrained general linear model, Commun. Statist. Theory Methods, 49 (2020), 1201–1216.
  • [17] H. J. Werner, C. Yapar, On equality constrained generalized least squares selections in the general possibly singular Gauss–Markov model: A projector theoretical approach, Linear Algebra Appl., 237/238 (1996), 359–393.
  • [18] X. Zhang, Y. Tian, On decompositions of BLUEs under a partitioned linear model with restrictions, Stat. Papers, 57 (2016), 345–364.
  • [19] Y. Tian, Equalities and inequalities for inertias of Hermitian matrices with applications, Linear Algebra Appl., 433 (2010a), 263–296.
  • [20] Y. Tian, Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method, Nonlinear Anal., 75 (2012), 717–734.
  • [21] I. S. Alalouf, G. P. H. Styan, Characterizations of estimability in the general linear model, Ann. Stat., 7 (1979), 194–200.
  • [22] A. S. Goldberger, Best linear unbiased prediction in the generalized linear regression model, J. Amer. Statist. Assoc., 57 (1962), 369–375.
  • [23] S. Puntanen, G. P. H. Styan, J. Isotalo, Matrix Tricks for Linear Statistical Models: Our Personal Top Twenty, Springer, Heidelberg, 2011.
  • [24] N. Güler, M. E. Büyükkkaya, Inertia and rank approach in transformed linear mixed models for comparison of BLUPs, Commun. Statist. Theory Methods, (2021), doi: 10.1080/03610926.2021.1967397.
  • [25] Y. Tian, A new derivation of BLUPs under random-effects model, Metrika, 78 (2015), 905–918.
  • [26] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413.
  • [27] Y. Tian, On properties of BLUEs under general linear regression models, J. Statist. Plann. Inference, 143 (2013), 771–782.

On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models

Yıl 2022, Cilt: 5 Sayı: 3, 192 - 200, 23.09.2022

Melek Eriş Büyükkaya Nesrin Güler

https://doi.org/10.33401/fujma.1134600
Cited By: 1

Öz

In this study, we consider a partitioned linear model with linear partial parameter constrains, known as a constrained partitioned linear model (CPLM), and its reduced models. A group of formulas on best linear unbiased predictors (BLUPs) and best linear unbiased estimators (BLUEs) in CPLM is derived via some quadratic matrix optimization methods, and further many basic properties of the predictors and estimators are established under some general assumptions. Our main purpose is to derive various inequalities and equalities for the comparison of covariance matrices of BLUPs and BLUEs under CPLM and its reduced models.

Anahtar Kelimeler

BLUP Correctly-reduced models Covariance matrix Rank

Kaynakça

  • [1] P. Bhimasankaram, R. SahaRay, On a partitioned linear model and some associated reduced models, Linear Algebra Appl., 264 (1997), 329–339.
  • [2] J. Grob, S. Puntanen, Estimation under a general partitioned linear model, Linear Algebra Appl., 321 (2000), 131–144.
  • [3] 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.
  • [4] J. K. Baksalary, P. R. Pordzik, Implied linear restrictions in the general Gauss–Markov model, J. Statist. Plann. Inference, 30 (1992), 237–248.
  • [5] A. R. Gallant, T. M. Gerig, Computations for constrained linear models, Econometrics, 12 (1) (1980), 59–84.
  • [6] S. J. Haslett, S. Puntanen, Equality of BLUEs or BLUPs under two linear models using stochastic restrictions, Stat. Papers, 51 (2010), 465–475.
  • [7] H. Jiang, J. Qian, Y. Sun, Best linear unbiased predictors and estimators under a pair of constrained seemingly unrelated regression models, Stat. Probab. Lett., 158 (2020), 108669.
  • [8] B. Jiang, Y. Sun, On the equality of estimators under a general partitioned linear model with parameter restrictions, Stat. Papers, 60 (2019), 273–292.
  • [9] B. Jiang, Y. Tian, Decomposition approaches of a constrained general linear model with fixed parameters, Electron. J. Linear Algebra, 32 (2017), 232–253.
  • [10] B. Jiang, Y. Tian, X. Zhang, On decompositions of estimators under a general linear model with partial parameter restrictions, Open Math., 15 (2017), 1300–1322.
  • [11] M. Liu, Y. Tian, R. Yuan, Statistical inference of a partitioned linear random-effects model, Commun. Statist. Theory Methods, (2021), doi: 10.1080/03610926.2021.1926509.
  • [12] R. Ma, Y. Tian, A matrix approach to a general partitioned linear model with partial parameter restrictions, Linear Multilinear Algebra, (2020), doi: 10.1080/03081087.2020.1804521.
  • [13] Y. Tian, On equalities of estimations of parametric functions under a general linear model and its restricted models, Metrika, 72 (3) (2010b), 313–330.
  • [14] Y. Tian, W. Guo, On comparison of dispersion matrices of estimators under a constrained linear model, Stat. Methods Appl., 25 (4) (2016), 623–649.
  • [15] Y. Tian, B. Jiang, Equalities for estimators of partial parameters under linear model with restrictions, J. Multivariate Anal., 143 (2016), 299–313.
  • [16] Y. Tian, J. Wang, Some remarks on fundamental formulas and facts in the statistical analysis of a constrained general linear model, Commun. Statist. Theory Methods, 49 (2020), 1201–1216.
  • [17] H. J. Werner, C. Yapar, On equality constrained generalized least squares selections in the general possibly singular Gauss–Markov model: A projector theoretical approach, Linear Algebra Appl., 237/238 (1996), 359–393.
  • [18] X. Zhang, Y. Tian, On decompositions of BLUEs under a partitioned linear model with restrictions, Stat. Papers, 57 (2016), 345–364.
  • [19] Y. Tian, Equalities and inequalities for inertias of Hermitian matrices with applications, Linear Algebra Appl., 433 (2010a), 263–296.
  • [20] Y. Tian, Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method, Nonlinear Anal., 75 (2012), 717–734.
  • [21] I. S. Alalouf, G. P. H. Styan, Characterizations of estimability in the general linear model, Ann. Stat., 7 (1979), 194–200.
  • [22] A. S. Goldberger, Best linear unbiased prediction in the generalized linear regression model, J. Amer. Statist. Assoc., 57 (1962), 369–375.
  • [23] S. Puntanen, G. P. H. Styan, J. Isotalo, Matrix Tricks for Linear Statistical Models: Our Personal Top Twenty, Springer, Heidelberg, 2011.
  • [24] N. Güler, M. E. Büyükkkaya, Inertia and rank approach in transformed linear mixed models for comparison of BLUPs, Commun. Statist. Theory Methods, (2021), doi: 10.1080/03610926.2021.1967397.
  • [25] Y. Tian, A new derivation of BLUPs under random-effects model, Metrika, 78 (2015), 905–918.
  • [26] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413.
  • [27] Y. Tian, On properties of BLUEs under general linear regression models, J. Statist. Plann. Inference, 143 (2013), 771–782.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Melek Eriş Büyükkaya 0000-0002-6207-5687

Nesrin Güler 0000-0003-3233-5377

Yayımlanma Tarihi 23 Eylül 2022
Gönderilme Tarihi 22 Haziran 2022
Kabul Tarihi 20 Ağustos 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 3

Kaynak Göster

APA Eriş Büyükkaya, M., & Güler, N. (2022). On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models. Fundamental Journal of Mathematics and Applications, 5(3), 192-200. https://doi.org/10.33401/fujma.1134600
AMA Eriş Büyükkaya M, Güler N. On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models. FUJMA. Eylül 2022;5(3):192-200. doi:10.33401/fujma.1134600
Chicago Eriş Büyükkaya, Melek, ve Nesrin Güler. “On Predictors and Estimators under a Constrained Partitioned Linear Model and Its Reduced Models”. Fundamental Journal of Mathematics and Applications 5, sy. 3 (Eylül 2022): 192-200. https://doi.org/10.33401/fujma.1134600.
EndNote Eriş Büyükkaya M, Güler N (01 Eylül 2022) On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models. Fundamental Journal of Mathematics and Applications 5 3 192–200.
IEEE M. Eriş Büyükkaya ve N. Güler, “On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models”, FUJMA, c. 5, sy. 3, ss. 192–200, 2022, doi: 10.33401/fujma.1134600.
ISNAD Eriş Büyükkaya, Melek - Güler, Nesrin. “On Predictors and Estimators under a Constrained Partitioned Linear Model and Its Reduced Models”. Fundamental Journal of Mathematics and Applications 5/3 (Eylül 2022), 192-200. https://doi.org/10.33401/fujma.1134600.
JAMA Eriş Büyükkaya M, Güler N. On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models. FUJMA. 2022;5:192–200.
MLA Eriş Büyükkaya, Melek ve Nesrin Güler. “On Predictors and Estimators under a Constrained Partitioned Linear Model and Its Reduced Models”. Fundamental Journal of Mathematics and Applications, c. 5, sy. 3, 2022, ss. 192-00, doi:10.33401/fujma.1134600.
Vancouver Eriş Büyükkaya M, Güler N. On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models. FUJMA. 2022;5(3):192-200.

Cited By

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https://doi.org/10.1080/03610926.2024.2314618
 Kapak Resmi İndir

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