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Original Articles

Comparing the BLUEs Under Two Linear Models

, &
Pages 2405-2418 | Received 26 Nov 2010, Accepted 02 Jun 2011, Published online: 05 Jun 2012

References

  • Albert , A. ( 1973 ). The Gauss–Markov theorem for regression models with possibly singular covariances . SIAM J. Appl. Math. 24 : 182 – 187 .
  • Baksalary , J. K. ( 1988 ). Criteria for the equality between ordinary least squares and best linear unbiased estimators under certain linear models . Can. J. Statist. 16 : 97 – 102 .
  • Baksalary , J. K. ( 2004 ). An elementary development of the equation characterizing best linear unbiased estimators . Lin. Alg. Applic. 388 : 3 – 6 .
  • Baksalary , J. K. , Kala , R. ( 1978 ). A bound for the Euclidean norm of the difference between the least squares and the best linear unbiased estimators . Ann. Statist. 6 : 1390 – 1393 .
  • Baksalary , J. K. , Kala , R. ( 1980 ). A new bound for the Euclidean norm of the difference between the least squares and the best linear unbiased estimators . Ann. Statist. 8 : 679 – 681 .
  • Baksalary , J. K. , Kala , R. ( 1981 ). Linear transformations preserving best linear unbiased estimators in a general Gauss–Markoff model . Ann. Statist. 9 : 913 – 916 .
  • Baksalary , J. K. , Kala , R. (1986). Linear sufficiency with respect to a given vector of parametric functions. J. Statist. Plann. Infer. 14:331–338.
  • Baksalary , J. K. , Mathew , T. ( 1986 ). Linear sufficiency and completeness in an incorrectly specified general Gauss–Markov model . Sankhyā Ser. A 48 : 169 – 180 .
  • Baksalary , O. M. , Trenkler , G. ( 2009 ). A projector oriented approach to the best linear unbiased estimator . Statist. Pap 50 : 721 – 733 .
  • Baksalary , J. K. , Rao , C. R. , Markiewicz , A. ( 1992 ). A study of the influence of the “natural restrictions” on estimation problems in the singular Gauss–Markov model . J. Statist. Plann. Infer. 31 : 335 – 351 .
  • Ben-Israel , A. , Greville , T. N. E. ( 2003 ). Generalized Inverses: Theory and Applications. , 2nd ed. New York : Springer .
  • Bloomfield , P. , Watson , G. S. ( 1975 ). The inefficiency of least squares . Biometrika 62 : 121 – 128 .
  • Christensen , R. ( 2002 ). Plane Answers to Complex Questions: The Theory of Linear Models. , 3rd ed. New York : Springer .
  • Drygas , H. ( 1970 ). The Coordinate-Free Approach to Gauss–Markov Estimation . Berlin : Springer .
  • Drygas , H. ( 1983 ). Sufficiency and completeness in the general Gauss–Markov model . Sankhyā Ser. A 45 : 88 – 98 .
  • Haberman , S. J. ( 1975 ). How much do Gauss–Markov and least square estimates differ? A coordinate-free approach . Ann. Statist. 3 : 982 – 990 .
  • Harville , D. A. ( 1997 ). Matrix Algebra from a Statistician's Perspective . New York : Springer .
  • Isotalo , J. , Puntanen , S. , Styan , G. P. H. ( 2008 ). A useful matrix decomposition and its statistical applications in linear regression . Commun. Statist. Theor. Meth. 37 : 1436 – 1457 .
  • Kempthorne , O. ( 1989 ). Comment [on Puntanen and Styan (1989)] . Amer. Statistician 43 : 161 – 162 .
  • Knott , M. ( 1975 ). On the minimum efficiency of least squares . Biometrika 62 : 129 – 132 .
  • Kruskal , W. ( 1968 ). When are Gauss–Markov and least squares estimators identical? A coordinate-free approach . Ann. Math. Statist. 39 : 70 – 75 .
  • Luati , A. , Proietti , T. ( 2011 ). On the equivalence of the weighted least squares and the generalised least squares estimators, with applications to kernel smoothing . Ann. Instit. Statist. Math. 63 : 851 – 871 .
  • Mäkinen , J. ( 2000 ). Bounds for the difference between a linear unbiased estimate and the best linear unbiased estimate . Phys. Chem. Earth – Part A: Solid Earth and Geodesy 25 : 693 – 698 .
  • Mäkinen , J. ( 2002 ). A bound for the Euclidean norm of the difference between the best linear unbiased estimator and a linear unbiased estimator . J. Geodesy 76 : 317 – 322 .
  • Markiewicz , A. , Puntanen , S. , Styan , G. P. H ( 2010 ). A note on the interpretation of the equality of OLSE and BLUE . Pak. J. Statist. 26 : 127 – 134 .
  • Mitra , S. K. , Moore , B. J. ( 1973 ). Gauss–Markov estimation with an incorrect dispersion matrix . Sankhyā, Ser. A 35 : 139 – 152 .
  • Puntanen , S. , Scott , A. J. ( 1996 ). Some further remarks on the singular linear model. Lin. Alg. Appli. 237/238:313–327 .
  • Puntanen, S., Styan, G. P. H. (1989). The equality of the ordinary least squares estimator and the best linear unbiased estimator (with discussion). Amer. Statistician 43:151–161 [Commented by O. Kempthorne on pp. 161–162 and by S. R. Searle on pp. 162–163, Reply by the authors on p. 164.]
  • Rao , C. R. ( 1967 ). Least squares theory using an estimated dispersion matrix and its application to measurement of signals. In: Le Cam, L. M., Neyman, J., eds. Proc. Fifth Berkeley Symposium on Mathematical Statistics and Probability: Berkeley, California, 1965/1966. Vol. 1. University of California Press, Berkeley, pp. 355–372 .
  • Rao , C. R. ( 1968 ). A note on a previous lemma in the theory of least squares and some further results . Sankhyā, Ser. A 30 : 259 – 266 .
  • Rao , C. R. (1971). Unified theory of linear estimation. Sankhyā, Ser. A 33:371–394. [Corrigendum (1972), 34:194, 477.]
  • Rao , C. R. ( 1973 ). Representations of best linear unbiased estimators in the Gauss–Markoff model with a singular dispersion matrix . J. Multivariate Anal. 3 : 276 – 292 .
  • Rao , C. R. , Mitra , S. K. ( 1971 ). Generalized Inverse of Matrices and Its Applications . New York : Wiley .
  • Searle , S. R. ( 1989 ). Comment [on Puntanen and Styan (1989)] . Amer. Statistician 43 : 162 – 163 .
  • Thomas , D. H. ( 1968 ). When do minimum variance estimators coincide? [Abstract] Ann. Math. Statist. 39:1365 .
  • Tian , Y. ( 2009 ). On equalities for BLUEs under misspecifiGauss–Markov models . Acta Mathematica Sinica, English Series 25 : 1907 – 1920 .
  • Tian , Y. , Takane , Y. ( 2008 ). Some properties of projectors associated with the WLSE under a general linear model . J. Multivariate Anal. 99 : 1070 – 1082 .
  • Tian , Y. , Takane , Y. ( 2009 ). On V-orthogonal projectors associated with a semi-norm . Ann. Instit. Statist. Math. 61 : 517 – 530 .
  • Trenkler , G. ( 1994 ). Characterizations of oblique and orthogonal projectors . In: Caliński , T. , Kala , R. , eds. Proceedings of the International Conference on Linear Statistical Inference LINSTAT '93 (Poznań, 1993) . Dordrecht : Kluwer , pp. 255 – 270 .
  • Watson , G. S. ( 1955 ). Serial correlation in regression analysis, I . Biometrika 42 : 327 – 341 .
  • Zmyślony , R. ( 1980 ). A characterization of best linear unbiased estimators in the general linear model . In: Klonecki , W. , Kozek , A. , Rosiński , J. , eds. Mathematical Statistics and Probability Theory: Proceedings of the Sixth International Conference . New York : Springer , pp. 365 – 373 .
  • Zyskind , G. ( 1967 ). On canonical forms, non-negative covariance matrices and best and simple least squares linear estimators in linear models . Ann. Mathemat. Statist. 38 : 1092 – 1109 .

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