ON EQUALITIES OF BLUES FOR A MULTIPLE RESTRICTED PARTITIONED LINEAR MODEL

Yunying Huang; Bing Zheng; Guoliang Chen

doi:10.11948/2018.1555

2018 Volume 8 Issue 5

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2018 > 8(5): 1555-1574

Next Article Previous Article

Yunying Huang, Bing Zheng, Guoliang Chen. ON EQUALITIES OF BLUES FOR A MULTIPLE RESTRICTED PARTITIONED LINEAR MODEL[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1555-1574. doi: 10.11948/2018.1555

Citation:

Yunying Huang, Bing Zheng, Guoliang Chen. ON EQUALITIES OF BLUES FOR A MULTIPLE RESTRICTED PARTITIONED LINEAR MODEL[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1555-1574. doi: 10.11948/2018.1555

ON EQUALITIES OF BLUES FOR A MULTIPLE RESTRICTED PARTITIONED LINEAR MODEL

1 School of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Dongchuan RD 500, Shanghai 200241, China;
2 School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

Fund Project:

Abstract

Abstract

For the multiple restricted partitioned linear model M={y,X₁ β₁ + …+ X_sβ_s | A₁β₁=b₁,…,A_sβ_s=b_s,Σ}, the relationships between the restricted partitioned linear model M and the corresponding s small restricted linear models M_i={y,X_iβ_i | A_iβ_i=b_i,Σ},i=1,…,s are studied. The necessary and sufficient conditions for the best linear unbiased estimators (BLUEs) under the full restricted model to be the sums of BLUEs under the s small restricted model are derived. Some statistical properties of the BLUEs are also described.
- Partitioned linear model /
- restricted models /
- BLUE /
- additive decomposition of estimation /
- Moore-Penrose inverse
MSC: 62H12;62J05;62J10

FullText(HTML)

References

[1]	I. S. Alauouf, G. P. H. Styan, Characterizations of estimability in the general linear model, Ann. Statist., 1979, 7(1), 194-200. Google Scholar
[2]	J. K. Baksalary, C. R. Rao, A. Markiewicz, A study of the influence of the natural restrictions on estimation problems in the singular Gauss-Markov model, J. Stat. Plann. Inference, 1992, 31(3), 335-351. Google Scholar
[3]	P. Bhimasankaram, R. Saharay, On a partitioned linear model and some associated reduced models, Linear Algebra Appl., 1997, 264(97), 329-339. Google Scholar
[4]	K. L. Chu, J. Isotalo, S. Puntanen, G. P. H. Styan, On decomposing the Watson efficiency of ordinary least squares in a partitioned weakly singular linear model, Sankhyā, Ser., 2004, 66(4), 634-651. Google Scholar
[5]	H. Drygas, The Coordinate-free Approach To Gauss-Markov Estimation, Springer-Heidelberg., 1970. Google Scholar
[6]	B. Dong, W. Guo, Y. Tian, On relations between BLUEs under two transformed linear models, J. Multivar Anal., 2014, 131(131), 279-292. Google Scholar
[7]	J. Groß, The general Gauss-Markov model with possibly singular dispersion matrix, Stat. Pap., 2004, 45(3), 311-336. Google Scholar
[8]	J. Groß, S. Puntanen, Estimations under a general partitioned linear model, Linear Algebra Appl., 2000, 321, 131-144. Google Scholar
[9]	Y. Huang, B. Zheng, The additive and block decompositions about the WLSEs of parametric functions for a multiple partitioned linear regression model, J. Multivar Anal., 2015, 133, 123-135. Google Scholar
[10]	B. Jiang, Y. Sun, On the equality of estimators under a general partitioned linear model with parameter restrictions, Stat. Pap., 2016, DOI:10.1007/s00362-016-0837-9. Google Scholar
[11]	C. Lu, S. Gan, Y. Tian, Some remarks on general linear model with new regressors, Statist. Probab. Lett., 2015, 97(97), 16-24. Google Scholar
[12]	X. Liu, Q. W. Wang, Equality of the BLUPs under the mixed linear model when random components and errors are correlated, J. Multivar Anal., 2013, 116(116), 297-309. Google Scholar
[13]	G. Marsaglia, G. P. H. Styan, Equalities and inequalities for ranks of matrices, Linear Multilinear Algebra., 1974, 2(3), 269-292. Google Scholar
[14]	M. Nurhonen, S. Puntanen, A property of partitioned generalized regression, Comm. Stat. Theory Methods, 1992, 21(6), 1579-1583. Google Scholar
[15]	R. Penrose, A generalized inverse for matrices, Proc. Camb. Phil. Soc., 1955, 51, 406-413. Google Scholar
[16]	C. R. Rao, Unified theory of linear estimation, Sankhyā, Ser. 1971, 33(4), 371-394. Google Scholar
[17]	C. R. Rao, Representations of best linear unbiased estimators in the GaussMarkoff model with a singular dispersion matrix, J. Multivar Anal., 1973, 3, 276-292. Google Scholar
[18]	G. J. Song, H. X. Chang, Equalities of various estimators in the general growth curve model and the restricted growth curve model, J. Stat. Plann. Inference, 2016, 169, 88-100. Google Scholar
[19]	G. J. Song, Q. W. Wang, On the weighted least-squares, the ordinary leastsquares and the best linear unbiased estimators under a restricted growth curve model, Stat. Pap., 2014, 55(2), 375-392. Google Scholar
[20]	Y. Tian, More on maximal and minimal ranks of Schur complements with applications, Appl. Math. Comput., 2004, 152(3), 675-692. Google Scholar
[21]	Y. Tian, Some decompositions of OLSEs and BLUEs under a partitioned linear model, Int. Stat. Rev., 2007, 75(2), 224-248. Google Scholar
[22]	Y. Tian, On an additive decomposition of the BLUE in a multiple partitioned linear model, J. Multivar Anal., 2009, 100(4), 767-776. Google Scholar
[23]	Y. Tian, M. Beisiegel, E. Dagebais, C. Haines, On the natural restrictions in the singular Gauss-Markov model, Stat. Pap., 2008, 49(3), 553-564. Google Scholar
[24]	Y. Tian, Z. Takane, On additive and block decompositions of WLSEs under a multiple partitioned regression model, Statistics., 2010, 44(4), 361-379. Google Scholar
[25]	Q. W. Wang, X. Liu, The Equalities of BLUPs for Linear Combinations Under Two General Linear Mixed Models, Comm. Stat. Theory Methods, 2013, 42(19), 3528-3543. Google Scholar
[26]	H. J. Werner, C. Yapar, A BLUE decomposition in the general linear regression model, Linear Algebra Appl., 1996, 237/238, 395-404. Google Scholar
[27]	H. J. Werner, C. Yapar, More on partitioned possibly restricted linear regression, Multivariate statistics and matrices in statistics. New trends in probability and statistics. Vol. 3, Proceedings of the 5th Tartu conference, Tartu, pp. 1995, 57-66. Google Scholar
[28]	B. Zhang, B. Liu, C. Lu, A study of the equivalence of the BLUEs between a partitioned singular linear model and its reduced singular linear models, Acta Math. Sinica Ser., 2004, 20(3), 557-568. Google Scholar
[29]	X. Zhang, Y. Tian, On decompositions of BLUEs under a partitioned linear model with restrictions, Stat. Pap., 2016, 57(2), 345-364. Google Scholar