Skip to main content
SpringerLink
Log in

A variable projection algorithm for estimating nonlinear systems of equations by iterated generalized least squares

  • Published:
Empirical Economics Aims and scope Submit manuscript

Summary

This note describes the application of the variable projection (VP) algorithm developed byGolub andPereyra [1973], and successively modified byKrogh [1974] andKaufman [1975] to the iterated generalized least squares estimation of nonlinear systems of equations whose parameters separate into a linear part and a nonlinear part.

The VP algorithm was originally applied to the least squares estimation of single-equation models having this structure. Recently an extension has been proposed [Corradi] for the estimation of seemingly unrelated nonlinear regressions, which has proved to be computationally more efficient than the standard methods as employed e.g. inGallant [1975].

In Section 1 we outline the proposed computational procedure and examine its relevant features, while in Section 2 we present some numerical results.

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

  • Bard, Y.: Comparison of gradient methods for the solution of nonlinear parameter estimation. SIAM J. Numer. Anal.7, 1970, 157–186.

    Google Scholar 

  • Barnett, W.A.: Maximum likelihood and iterated Aitken estimation of nonlinear systems of equations. J.A.S.A.71, 1976, 354–360.

    Google Scholar 

  • Berndt, E. V., B.H. Hall, R.E. Hall, andJ.A. Hausman: Estimation and inference in nonlinear structural models. Annals of Economic and Social Measurement3, 1974, 653–665.

    Google Scholar 

  • Carlevaro, F., andE. Rossier: Le programme LINEX pour l'estimation des parametres du systeme lineaire de depenses. Faculté de Sciences Economiques et Sociales, Université de Grenoble, Centre d'Econometrie, Cahier 16.6.1970.

  • Corradi, C.: An efficient computational procedure for estimating seemingly unrelated nonlinear regressions. Seminari di Econometria, Università di Modena, 1975.

  • Gallant, A.R.: Seemingly unrelated nonlinear regressions. Journal of Econometrics3, 1975, 35–50.

    Google Scholar 

  • Golub, G.H., andV. Pereyra: The differentiation of pseudoinverses and nonlinear least squares problems whose variables separate. SIAM J. Numer. Anal.10, 1973, 413–432.

    Google Scholar 

  • Hanson, R.J., andC.L. Lawson: Solving least squares problems. Englewood Cliffs, 1974.

  • Kaufman, L.: A variable projection method for solving separable nonlinear least squares problems. BIT15, 1975, 49–57.

    Google Scholar 

  • Krogh, F.T.: Efficient implementation of a variable projection algorithm for nonlinear least squares problems. Comm. ACM17, 1974, 167–169.

    Google Scholar 

  • Powell, A.A.: Empirical analitics of demand systems. Lexington, 1974.

Download references

Author information

Authors and Affiliations

  1. Divisione Gestione Sistema Informativo, Comitato Nazionale per L'Energia Nucleare, Bologna

    C. Corradi

  2. Istituto di Scienze Economiche, Università di Bologna, I-Bologna

    C. Corradi

Authors
  1. C. Corradi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Corradi, C. A variable projection algorithm for estimating nonlinear systems of equations by iterated generalized least squares. Empirical Economics 2, 101–108 (1977). https://doi.org/10.1007/BF01767475

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01767475

Keywords

Search

Navigation