Skip to main content

Advertisement

Log in

A note on the equality of the OLSE and the BLUE of the parametric function in the general Gauss–Markov model

  • Note
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

In this note we consider the equality of the ordinary least squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of the estimable parametric function in the general Gauss–Markov model. Especially we consider the structures of the covariance matrix V for which the OLSE equals the BLUE. Our results are based on the properties of a particular reparametrized version of the original Gauss–Markov model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Anderson TW (1948) On the theory of testing serial correlation. Skandinavisk Aktuarietidskrift 31:88–116

    Google Scholar 

  • Drygas H (1970) The coordinate-free approach to Gauss–Markov estimation. Springer, Heidelberg

    MATH  Google Scholar 

  • Gross J, Trenkler G, Werner HJ (2001) The equality of linear transforms of the ordinary least squares estimator an the best linear unbiased estimator. Sankhyā Ser A 63:118–127

    MATH  MathSciNet  Google Scholar 

  • Marsaglia G, Styan GPH (1974) Equalities and inequalities for ranks of matrices. Linear Multilinear Algebra 2:269–292

    Article  MathSciNet  Google Scholar 

  • Peixoto JL (1993) Four equivalent definitions of reparametrizations and restrictions in linear model. Commun Stat Theory Methods 22:283–299

    MATH  MathSciNet  Google Scholar 

  • Puntanen S, Styan GPH (1989) The equality of the ordinary least squares estimator and the best linear unbiased estimator [with comments by Oscar Kempthorne & by Shayle R. Searle and with “Reply” by the authors]. Am Stat 43:153–164

    Google Scholar 

  • Rao CR (1967) Least squares theory using an estimated dispersion matrix and its application to measurement of signals. In: Le Cam LM, Neyman J (eds) Proceedings of the 5th Berkeley symposium on mathematical statistics and probability: Berkeley, California, 1965/1966, vol 1. University of California Press, Berkeley, pp 355–372

  • Rao CR (1968) A note on a previous lemma in the theory of least squares and some further results. Sankhyā Ser A 30:245–252

    Google Scholar 

  • Rao CR (1973) Representations of best linear unbiased estimators in the Gauss–Markoff model with a singular dispersion matrix. J Multivariate Anal 3:276–292

    Article  MATH  MathSciNet  Google Scholar 

  • Rao CR, Mitra SK (1971) Generalized inverse of matrices and its applications. Wiley, New York

    MATH  Google Scholar 

  • Sengupta D, Jammalamadaka SR (2003) Linear models: an integrated approach. World Scientific, Singapore

    MATH  Google Scholar 

  • Zyskind G (1967) On canonical forms, non-negative covariance matrices and best and simple least squares linear estimators in linear models. Ann Math Stat 38:1092–1109

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Simo Puntanen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Isotalo, J., Puntanen, S. A note on the equality of the OLSE and the BLUE of the parametric function in the general Gauss–Markov model. Stat Papers 50, 185–193 (2009). https://doi.org/10.1007/s00362-007-0055-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-007-0055-6

Keywords

Mathematics Subject Classification (2000)

Navigation