Skip to main content
SpringerLink
Log in

On best affine prediction

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

Abstract

The theory of best affine prediction (BAP) is extended to the vector case with possibly singular variance matrix of the predictor variable. The theory is then applied to derive Thomson’s classical predictor for factor scores, allowing for a singular variance matrix of the factors. The results are formulated in a free distribution setting. Further, Bartlett’s estimator is considered and compared with Thomson’s predictor.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anderson, T.W. (1994). An Introduction to Multivariate Statistical Analysis (Second Edition), John Wiley.

  2. Astrom, K.J. (1970). Introduction to Stochastic Control Theory, Academic Press

  3. Bartlett, M.S. (1937). The statistical conception of mental factors, British Journal of Mathematical and Statistical Psychology, 28, 97–104.

    Google Scholar 

  4. Greene, W. H. 1997, Econometric Analysis (Third Edition), Prentice-Hall

  5. Krijnen, W.P., Wansbeek, T., and J. M.F. ten Berge. (1996). Best linear predictors for factor scores, Commun. Statist. — Theory Meth., 25 (12), 3013–3025.

    Article  MATH  Google Scholar 

  6. Löwner, K. (1934). Über monotone Matrixfunktionen. Mathematische Zeitschrift, 38, 177–216.

    Article  MathSciNet  Google Scholar 

  7. Magnus, J. R. and Neudecker, H. 1999. Matrix Differential Calculus with Applications in Statistics and Econometrics (Revised Edition), John Wiley.

  8. Thomson, G. (1951), The Factorial Analysis of Human Ability (Fifth Edition), University of London Press.

Download references

Author information

Authors and Affiliations

  1. Cesaro, Oosterstraat 13, 1741, GH Schagen, The Netherlands

    Heinz Neudecker

  2. Department of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, 08005, Barcelona, Spain

    Albert Satorra

Authors
  1. Heinz Neudecker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Albert Satorra
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The authors are thankful to the two referees, one for a suggestion that led to the Addendum of the paper, and the other one for several very useful remarks. Research supported by the Spanish grant BEC2000-0983.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Neudecker, H., Satorra, A. On best affine prediction. Statistical Papers 44, 257–266 (2003). https://doi.org/10.1007/s00362-003-0150-2

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-003-0150-2

Keywords

Search

Navigation