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ArticleOriginal scientific text

Title

Decomposing matrices with Jerzy K. Baksalary

Authors 1, 1, 2

Affiliations

  1. Department of Mathematics and Statistics, FI-33014 University of Tampere, Finland
  2. Department of Mathematics and Statistics, McGill University, 805 ouest rue Sherbrooke Street West, Montréal (Québec), Canada H3A 2K6

Abstract

In this paper we comment on some papers written by Jerzy K. Baksalary. In particular, we draw attention to the development process of some specific research ideas and papers now that some time, more than 15 years, has gone after their publication.

Keywords

ENG
BLUE, BLUE's covariance matrix, canonical correlations, generalized inverse, linear model, linear sufficiency, OLSE, orthogonal projector, residuals

Bibliography

  1. C.W. Ahlers and T.O. Lewis, Linear estimation with a positive semidefinite covariance matrix, Industrial Mathematics 21 (1971), 23-27.
  2. I.S. Alalouf, Comments on a paper by Ahlers and Lewis, Industrial Mathematics, 25 (1975a), 97-104.
  3. I.S. Alalouf, Estimability and testability in linear models, Ph.D. Dissertation, Department of Mathematics, McGill University, Montréal 1975b.
  4. J.K. Baksalary, A study of the equivalence between a Gauss-Markoff model and its augmentation by nuisance parameters, Mathematische Operationsforschung und Statistik, Series Statistics 15 (1984), 3-35.
  5. J.K. Baksalary, Algebraic characterizations and statistical implications of the commutativity of orthogonal projectors, Proceedings of the Second International Tampere Conference in Statistics: University of Tampere, Tampere, Finland, 1-4 June 1987 (Tarmo Pukkila and Simo Puntanen, eds.), Department of Mathematical Sciences/Statistics, University of Tampere, Tampere, Finland, vol. A 184 (1987), 113-142.
  6. J.K. Baksalary and R. Kala, A note on Ahlers and Lewis' representation of the best linear unbiased estimator in the general Gauss-Markoff model, (Robert Bartoszyński, Jacek Koronacki and Ryszard Zieliński, eds.), PWN-Polish Scientific Publishers, Warsaw Banach Center Publications, Mathematical Statistics vol. 6 (1980), 17-21. [Presented to the Semester Mathematical Statistics: September 15-December 18, 1976.]
  7. J.K. Baksalary and R. Kala Linear transformations preserving best linear unbiased estimators in a general Gauss-Markoff model, The Annals of Statistics 4 (1981), 913-916. [A preliminary version of this paper was presented at the 6th International Conference on Mathematical Statistics in Wisła, Poland, on December 1978.]
  8. J.K. Baksalary and R. Kala, Linear sufficiency with respect to a given vector of parametric functions, Journal of Statistical Planning and Inference 14 (1986), 331-338.
  9. J.K. Baksalary and T. Mathew, Rank invariance criterion and its application to the unified theory of least squares, Linear Algebra and its Applications 127 (1990), 393-401.
  10. J.K. Baksalary, S. Puntanen and G.P.H. Styan, A property of the dispersion matrix of the best linear unbiased estimator in the general Gauss-Markov model, Sankhyā, Series A, 52 (1990), 279-296.
  11. J.K. Baksalary, S. Puntanen and H. Yanai, Canonical correlations associated with symmetric reflexive generalized inverses of the dispersion matrix, Linear Algebra and its Applications 176 (1992), 61-74.
  12. G.A. Barnard, The logic of least squares, Journal of the Royal Statistical Society, Series B (Methodological) 25 (1963), 124-127.
  13. D.R. Cox and D.V. Hinkley, Theoretical Statistics, Chapman and Hall, London 1974.
  14. H. Drygas, Sufficiency and completeness in the general Gauss-Markov model, Sankhyā, Series A, 45 (1983), 88-98.
  15. S.J. Haberman, How much do Gauss-Markov and least squares estimates differ? A coordinate-free approach, The Annals of Statistics 3 (1975), 982-990.
  16. D.A. Harville, Matrix Algebra From a Statistician's Perspective, Springer, New York 1997.
  17. J. Isotalo, Linear estimation and prediction in the general Gauss-Markov model, Ph.D. Dissertation, Department of Mathematics, Statistics and Philosophy, University of Tampere, Tampere, Finland: Acta Universitatis Tamperensis, vol. 1242; Acta Electronica Universitatis Tamperensis, vol. 636 (2007).
  18. J. Isotalo and S. Puntanen, Linear sufficiency and completeness in the partitioned linear model, Acta et Commentationes Universitatis Tartuensis de Mathematica 10 (2006a), 53-67. Paper [1] of Isotalo (2007).
  19. J. Isotalo and S. Puntanen, Linear sufficiency and completeness in the context of estimating the parametric function in the general Gauss-Markov model (2006b). Paper [2] of Isotalo (2007), submitted for publication.
  20. J. Isotalo and S. Puntanen, Linear prediction sufficiency for new observations in the general Gauss-Markov model, Communications in Statistics: Theory and Methods 35 (2006c), 1011-1023. Paper [3] of Isotalo (2007).
  21. J. Isotalo, S. Puntanen and George P.H. Styan, A useful matrix decomposition and its statistical applications in linear regression, Communications in Statistics: Theory and Methods (2008), in press, 22 pp. Paper [11] of Isotalo (2007).
  22. Ch.G. Khatri, Some properties of BLUE in a linear model and canonical correlations associated with linear transformations, Journal of Multivariate Analysis 34 (1990), 211-226.
  23. S. Puntanen, Properties of the covariance matrix of the BLUE in the general linear model, Pacific Statistical Congress: Auckland, New Zealand, May 1985 (I.S. Francis, B.F.J. Manly and F.C. Lam, eds.), Elsevier Science Publishers, Amsterdam (1986), 425-430.
  24. S. Puntanen, On the relative goodness of ordinary least squares estimation in the general linear model Ph.D. Dissertation, Department of Mathematical Sciences, University of Tampere, Tampere, Finland: Acta Universitatis Tamperensis, Series A, vol. 216 (1987).
  25. S. Puntanen and A.J. Scott, Some further remarks on the singular linear model, Linear Algebra and its Applications 237/238 (1996), 313-327.
  26. S. Puntanen and G.P.H. Styan, More properties of the covariance matrix of the BLUE in the general linear model, (1986), Unpublished manuscript, revised and published as Baksalary, Puntanen and Styan (1990).
Discussiones Mathematicae Probability and Statistics
2008/28/1
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Pages:
91-111
Main language of publication
English
Received
2007-12-14
Published
2008

DOI: 10.7151/dmps.1094

Exact and natural sciences