On Rank Estimation In Symmetric Matrices: The Case Of Indefinite Matrix Estimators
AbstractIn this paper we consider estimating the rank of 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 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 sum of eigenvalues of the matrix estimator. We discuss two applications where rank estimation in symmetric matrices is of interest, and we also provide a small simulation study.The first author acknowledges the support of an Alfred P. Sloan Foundation Research Fellowship and NSF Grant SES-0196372. We thank the co-editor and the two referees for useful comments and suggestions. CEMPRE Centro de Estudos Macroecon micos e Previs o is supported by the Funda o para a Ci ncia e a Tecnologia, Portugal, through the Programa Operacional Ci ncia, Tecnologia e Inova o (POCTI) of the Quadro Comunit rio de Apoio III, which is financed by FEDER and Portuguese funds.
Download InfoIf 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.
Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 23 (2007)
Issue (Month): 06 (December)
Contact details of provider:
Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Fax: +44 (0)1223 325150
Web page: http://journals.cambridge.org/jid_ECTProvider-Email:email@example.com
Other versions of this item:
- Stephen G. Donald & Natércia Fortuna & Vladas Pipiras, 2005. "On rank estimation in symmetric matrices: the case of indefinite matrix estimators," FEP Working Papers 167, Universidade do Porto, Faculdade de Economia do Porto.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
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.:
- 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.
- Robin, J-M & Smith, RJ, 2000.
"Tests of rank,"
Open Access publications from University College London
http://discovery.ucl.ac.u, University College London.
- Kleibergen, F.R. & Paap, R., 2003.
"Generalized Reduced Rank Tests using the Singular Value Decomposition,"
Econometric Institute Report
EI 2003-01, Erasmus University Rotterdam, Econometric Institute.
- 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.
- Frank Kleibergen & Richard Paap, 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Tinbergen Institute Discussion Papers 03-003/4, Tinbergen Institute.
- Richard Paap & Frank Kleibergen, 2004. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Society 2004 Australasian Meetings 195, Econometric Society.
- Bura, Efstathia & Cook, R. Dennis, 2003. "Rank estimation in reduced-rank regression," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 159-176, October.
- Fortuna, Natercia, 2008.
"Local rank tests in a multivariate nonparametric relationship,"
Journal of Econometrics,
Elsevier, vol. 142(1), pages 162-182, January.
- Natércia Fortuna, 2004. "Local rank tests in a multivariate nonparametric relationship," FEP Working Papers 137, Universidade do Porto, Faculdade de Economia do Porto.
- Natercia Fortuna, 2004. "Local rank tests in a multivariate nonparametric relationship," Econometric Society 2004 North American Summer Meetings 446, Econometric Society.
- repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
- 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.
- 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.
- Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," Econometrics 0307007, EconWPA.
- Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
- Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
- Donkers, A.C.D. & Schafgans, M., 2003.
"A Derivative Based Estimator for Semiparametric Index Models,"
2003-22, Tilburg University, Center for Economic Research.
- Donkers, A.C.D. & Schafgans, M., 2003. "A derivative based estimator for semiparametric index models," Econometric Institute Report EI 2003-08, Erasmus University Rotterdam, Econometric Institute.
- 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.
- Gonzalo Camba-Mendez & George Kapetanios & Richard J. Smith & Martin Weale, 1999. "Tests of Rank in Reduced Rank Regression Models," NIESR Discussion Papers 150, National Institute of Economic and Social Research.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters).
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.