On Rank Estimation In Symmetric Matrices: The Case Of Indefinite Matrix Estimators
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.
(This abstract was borrowed from another version of this item.)
Volume (Year): 23 (2007)
Issue (Month): 06 (December)
|Contact details of provider:|| Postal: |
Web page: http://journals.cambridge.org/jid_ECTEmail:
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.:
- Richard Paap & Frank Kleibergen, 2004.
"Generalized Reduced Rank Tests using the Singular Value Decomposition,"
Econometric Society 2004 Australasian Meetings
195, Econometric Society.
- 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.
- Kleibergen, F.R. & Paap, R., 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Institute Research Papers EI 2003-01, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- 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.
- 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.
- Robin, J.M. & Smith, R.J., 1995.
"Tests of Rank,"
Cambridge Working Papers in Economics
9521, Faculty of Economics, University of Cambridge.
- Natércia Fortuna, 2004.
"Local rank tests in a multivariate nonparametric relationship,"
FEP Working Papers
137, Universidade do Porto, Faculdade de Economia do Porto.
- Fortuna, Natercia, 2008. "Local rank tests in a multivariate nonparametric relationship," Journal of Econometrics, Elsevier, vol. 142(1), pages 162-182, January.
- Natercia Fortuna, 2004. "Local rank tests in a multivariate nonparametric relationship," Econometric Society 2004 North American Summer Meetings 446, Econometric Society.
- 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 Research Papers EI 2003-08, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- repec:dgr:uvatin:20030003 is not listed on IDEAS
- Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
- Bura, Efstathia & Cook, R. Dennis, 2003. "Rank estimation in reduced-rank regression," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 159-176, October.
- repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
- 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.
- 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.
- Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," Econometrics 0307007, EconWPA.
- 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.
- Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
- repec:dgr:kubcen:200322 is not listed on IDEAS
- 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.
When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:23:y:2007:i:06:p:1217-1232_07. 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: (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.