Advanced Search
MyIDEAS: Login to save this paper or follow this series

On rank estimation in symmetric matrices: the case of indefinite matrix estimators

Contents:

Author Info

  • Stephen G. Donald

    ()
    (University of Texas at Austin)

  • Natércia Fortuna

    ()
    (CEMPRE, Faculdade de Economia do Porto)

  • Vladas Pipiras

    ()
    (University of North Carolina at Chapel Hill)

Abstract

We focus on the problem of rank estimation in an unknown symmetric matrix based on a symmetric, asymptotically normal estimator of the matrix. The related positive definite limit covariance matrix is assumed to be estimated consistently, and to have either a Kronecker product or an arbitrary structure. These assumptions are standard although they also exclude the case when the matrix estimator is positive or negative semidefinite. We adapt and reexamine here some available rank tests, and introduce a new rank test based on the eigenvalues of the matrix estimator. We discuss several applications where rank estimation in symmetric matrices is of interest, and also provide a small simulation study and an application.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.fep.up.pt/investigacao/workingpapers/05.02.14_WP167_natercia.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Universidade do Porto, Faculdade de Economia do Porto in its series FEP Working Papers with number 167.

as in new window
Length: 27 pages.
Date of creation: Feb 2005
Date of revision:
Handle: RePEc:por:fepwps:167

Contact details of provider:
Postal: Rua Dr. Roberto Frias, 4200 PORTO
Phone: 351-22-5571100
Fax: 351-22-5505050
Email:
Web page: http://www.fep.up.pt/
More information through EDIRC

Related research

Keywords: rank; symmetric matrix; eigenvalues; matrix decompositions; estimation; asymptotic normality; consistency;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Efstathia Bura & R. Dennis Cook, 2001. "Estimating the structural dimension of regressions via parametric inverse regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 393-410.
  2. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," EERI Research Paper Series EERI_RP_2003_04, Economics and Econometrics Research Institute (EERI), Brussels.
  3. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
  4. n/a, 2001. "A Comparison of Personal Sector Saving Rates in the UK, US and Italy," NIESR Discussion Papers 150, National Institute of Economic and Social Research.
  5. Bura, Efstathia & Cook, R. Dennis, 2003. "Rank estimation in reduced-rank regression," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 159-176, October.
  6. Stephen G. Donald, 1997. "Inference Concerning the Number of Factors in a Multivariate Nonparametric Relationship," Econometrica, Econometric Society, vol. 65(1), pages 103-132, January.
  7. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
  8. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
  9. Robin, J.M. & Smith, R.J., 1995. "Tests of Rank," Cambridge Working Papers in Economics 9521, Faculty of Economics, University of Cambridge.
  10. Natercia Fortuna, 2004. "Local rank tests in a multivariate nonparametric relationship," Econometric Society 2004 North American Summer Meetings 446, Econometric Society.
  11. Donkers, A.C.D. & Schafgans, M., 2003. "A Derivative Based Estimator for Semiparametric Index Models," Discussion Paper 2003-22, Tilburg University, Center for Economic Research.
  12. repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
  13. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," Econometrics 0307007, EconWPA.
  14. Camba-Mendez, Gonzalo, et al, 2003. "Tests of Rank in Reduced Rank Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 145-55, January.
  15. Cragg, John G. & Donald, Stephen G., 1993. "Testing Identifiability and Specification in Instrumental Variable Models," Econometric Theory, Cambridge University Press, vol. 9(02), pages 222-240, April.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Majid M. Al-Sadoon, 2014. "A general theory of rank testing," Economics Working Papers 1411, Department of Economics and Business, Universitat Pompeu Fabra.
  2. Jin, Fei & Lee, Lung-fei, 2013. "Cox-type tests for competing spatial autoregressive models with spatial autoregressive disturbances," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 590-616.
  3. Ahn, Seung C. & Perez, M. Fabricio, 2010. "GMM estimation of the number of latent factors: With application to international stock markets," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 783-802, September.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:por:fepwps:167. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.