Advanced search
Publication Cover
Communications in Statistics - Theory and Methods Volume 52, 2023 - Issue 21
Submit an article Journal homepage
769
Views
1
CrossRef citations to date
0
Altmetric
Article

Properties of BLUEs in full versus small linear models

Stephen J. Hasletta Research School of Finance, Actuarial Studies and Statistics, The Australian National University, Canberra, Australia;b Centre for Public Health Research, Massey University, Wellington, New Zealand;c School of Fundamental Sciences, Massey University, Palmerston North, New ZealandORCID Iconhttps://orcid.org/0000-0002-2775-5468
ORCID Icon,
Augustyn Markiewiczd Department of Mathematical and Statistical Methods, Poznań University of Life Sciences, Poznań, PolandORCID Iconhttps://orcid.org/0000-0001-5473-3419
ORCID Icon &
Simo Puntanene Faculty of Information Technology and Communication Sciences, Tampere University, Tampere, FinlandCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-6776-0173
ORCID Icon
Pages 7684-7698 | Received 12 Aug 2021, Accepted 09 Mar 2022, Published online: 29 Mar 2022

References

  • Groß, J., and S. Puntanen. 2000. Estimation under a general partitioned linear model. Linear Algebra and Its Applications 321, 131–44. doi:10.1016/S0024-3795(00)00028-8.
  • Güler, N., S. Puntanen, and H. Özdemir. 2014. On the BLUEs in two linear models via C.R. Rao’s Pandora’s Box. Communications in Statistics - Theory and Methods, 5, 43, 921–31. doi:10.1080/03610926.2013.826366.
  • Haslett, S. J. 1996. Updating linear models with dependent errors to include additional data and/or parameters. Linear Algebra and Its Applications 237(238):329–49.
  • Haslett, S. J., A. Markiewicz, and S. Puntanen. 2020. Properties of BLUEs and BLUPs in full vs. small linear models with new observations. In Recent developments in multivariate and random matrix analysis: Festschrift in honour of Dietrich von Rosen, eds. T. Holgersson and M. Singull, 123–46. Cham: Springer.
  • Haslett, S. J., and S. Puntanen. 2010. Effect of adding regressors on the equality of the BLUEs under two linear models. Journal of Statistical Planning and Inference 140, 104–10. doi:10.1016/j.jspi.2009.06.010.
  • Lu, C., S. Gan, and Y. Tian. 2015. Some remarks on general linear model with new regressors. Statistics & Probability Letters, 97, 16–24. doi:10.1016/j.spl.2014.10.015.
  • Markiewicz, A, and S. Puntanen. 2019. Further properties of the linear sufficiency in the partitioned linear model. In Matrices, statistics and big data, eds. S. E. Ahmed, F. Carvalho and S. Puntanen, 1–22. Cham: Springer.
  • Marsaglia, G, and G. P. H. Styan. 1974. Equalities and inequalities for ranks of matrices. Linear Multilinear Algebra 2:269–92.
  • Mitra, S. K, and B. J. Moore. 1973. Gauss–Markov estimation with an incorrect dispersion matrix. Sankhyā Series A 35:139–52.
  • Puntanen, S., G. P. H. Styan, and J. Isotalo. 2011. Matrix tricks for linear statistical models: our personal top twenty. Heidelberg: Springer.
  • Rao, C. R. 1973. Representations of best linear estimators in the Gauss–Markoff model with a singular dispersion matrix. Journal of Multivariate Analysis 3, 276–92. doi:10.1016/0047-259X(73)90042-0.
  • Rao, C. R. 1974. Projectors, generalized inverses and the BLUE’s. Journal of the Royal Statistical Society: Series B 36:442–8.
  • Rao, C. R, and S. K. Mitra. 1971. Generalized inverse of matrices and its applications. New York: Wiley.
  • Sengupta, D, and S. R. Jammalamadaka. 2003. Linear models: An integrated approach. River Edge: World Scientific.
  • Tian, Y. 2013. On properties of BLUEs under general linear regression models. Journal of Statistical Planning and Inference 43, 771–82. doi:10.1016/j.jspi.2012.10.005.
  • Tian, Y., and X. Zhang. 2016. On connections among OLSEs and BLUEs of whole and partial parameters under a general linear model. Statistics & Probability Letters 112, 105–12. doi:10.1016/j.spl.2016.01.019.
  • Werner, H.J., and C. Yapar. 1996. A BLUE decomposition in the general linear regression model. Linear Algebra and its Applications 237-238, 395–404. doi:10.1016/0024-3795(95)00542-0.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.