DİK PARÇALANMIŞ LİNEER MODEL ve BU MODELİN İNDİRGENMİŞ MODELLERİ ALTINDA OLSE'Ieri ile İLİŞKİLİ BAZI WATSON ETKİNLİK AYRIŞIMLARI

Year 2013, Volume: 6 Issue: 1, 77 - 86, 01.06.2013

Esma Kesriklioğlu Esma Kesriklioğlu Nesrin Güler

Abstract

Çalrşmada, dik parçalanmış M = {y,Xßx + X2ß2V} lineer modeli ve bu
modelin bazı indirgenmiş modelleri ele alınmıştır. Ele alman modeller
altında parametrelerin alışılmış en küçük kareler talimin edicileri (OLSEs) ile
ilgili bazı Watson Etkinlik ayrışımları verilmiştir. Elde edilen sonuçlar Chu,
Isotalo, Puntanen ve Styan, (2004) tarafından verilen bazı sonuçların X1 ve X2
matrislerinin dik ve V- dik olma koşulları altında özel bir durumudur.

Keywords

BLUE, OLSE, dik parçalanmış lineer model, indirgenmiş model, Watson Etkinliği.

References

• Aitken, A.C. On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55. 1935.
• Alalouf, I. S. & Styan, G. P. H. Characterizations of estimability in the general linear model. The Annals of Statistics, 7, 194-200, 1979.
• Anderson, T. W. On the theory of testing serial correlation, Skandinavisk Aktuarietidskrift, 31, 88-116, 1948.
• Baksalary, O. M. & Trenkler, G. A projector oriented approach to the best linear unbiased estimator. Statistical Papers, 50, 721-733, 2009.
• Balakrishnan, N. & Rao, C.R. Some efficiency properties of best linear unbiased estimators. J. Statist. Plann. Inf. 113, 551-555, 2003.
• Chu, K.L., Isotalo, J., Puntanen, S. & Styan, G.P.H. On decomposing the Watson efficiency of ordinary least squares in a partitioned weakly singular linear model. Sankhyä, 66, 634-651. 2004.
• Chu, K.L., Isotalo, J., Puntanen, S. & Styan, G.P.H. Some further results concerning the decomposition of the Watson efficiency in partitioned linear models. Sankhyä, 67, 74-89. 2005.
• Chu, K.L., Isotalo, J., Puntanen, S. & Styan, G.P.H. The efficiency factorization multiplier for the Watson efficiency in partitioned linear models: some examples and a literature review. Journal of Statistical Planning and Inference, 137, 3336-3351. 2007.
• Chu, K.L., Isotalo, J., Puntanen, S. & Styan, G.P.H. Inequalities and equalities for the generalized efficiency function in orthogonally partitioned linear models. In Inequalities and Applications (T. M. Rassias & D. Andrica, eds.), Cluj Univ. Press, pp. 13-69. 2008.
• Chu, K.L., & Styan, G.P.H. On the efficiency of OLS in simple linear regression, with special reference to the situation where the OLS and GLS regression lines are parallel. Report 2003-04, Dept. of Mathematics and Statistics, McGill University, Montr eal (Qu ebec), Canada, November 2003.
• Fisher, R. A. On the mathematical foundations of theoretical statistics, Philos. Trans. Roy. Soc. London Ser. A: 222, 309368, 1922.
• Groß, J. and Puntanen, S. Estimation under a general partitioned linearmodel. Linear Algebra Appl.321, 131-144. 2000.
• Liski, E. P., Puntanen, S. & Wang, S.G. Bounds for the trace of the difference of the covariance matrices of the OLSE and BLUE. Lin. Alg. App., 176, 121-130. 1992.
• Liu, S. Efficiency comparisons between the OLSE and the BLUE in a singular linear model. Journal of Statistical Planning and Inference, 84, 191-200. 2000.
• Liu, S. & King, M. L. Two Kantorovich-type inequalities and efficiency comparisons between the OLSE and BLUE. J. Inequalities and Application, 7,169-177. 2002.
• Odell, P.L. Gauss-Markov Theorem. In Kotz. Johnson and read, 113,314-316, 1983.
• Puntanen, S. & Styan,, G.P.H. The equality of the ordinary least squares estimator and the best linear unbiased estimator (with discussion). Amer. Statist. 43, 153-164. 1989.
• Puntanen, S., Styan, and Isotalo, J. Matrix Tricks for Linear Statistical Models, Our Personal Top Twenty, Springer, Heidelberg, 2011.
• Rao, C.R. Least squares theory using an estimated dispersion matrix and its application to measurement of signals. Proc. Fifth Berkeley Symposium on Mathe-matical Statistics and Probability: Berkeley, California, 1965/1966, vol. 1, L.M. Le Cam and J. Neyman, eds., Univ. of California Press, Berkeley, 355-372. 1967.
• Rao, C. R. A note on a previous lemma in the theory of least squares and some further results. Sankhya, Ser. A, 30, 259266. 1968.
• 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.
• Seber, G.A.F., A Matrix Handbook for Statisticians, John Wiley, New York, 2007.
• Tian, Y. & Wiens, D. P. On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model. Statistics & Probability Letters, 76, 1265-1272. 2006.
• Watson, G. S. Serial correlation in regression analysis. Ph.D. Thesis, Dept. of Experimental Statistics, North Carolina State College, Raleigh. 1951.
• Wilks, S.S. Certain generalizations in the analysis of variance. Biometrika, 24, 471-494, 1932.