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.
|Date of creation:||Feb 2005|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.fep.up.pt/
More information through EDIRC
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.:
- 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.
- Robin, J.M. & Smith, R.J., 1995.
"Tests of Rank,"
Cambridge Working Papers in Economics
9521, Faculty of Economics, University of Cambridge.
- 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.
- 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.
- Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
- Frank Kleibergen & Richard Paap, 2003.
"Generalized Reduced Rank Tests using the Singular Value Decomposition,"
Tinbergen Institute Discussion Papers
03-003/4, Tinbergen 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.
- 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.
- Richard Paap & Frank Kleibergen, 2004. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Society 2004 Australasian Meetings 195, Econometric Society.
- Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
- 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.
- 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.
- repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
- Bura, Efstathia & Cook, R. Dennis, 2003. "Rank estimation in reduced-rank regression," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 159-176, October.
- Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," Econometrics 0307007, EconWPA.
- 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," EERI Research Paper Series EERI_RP_2003_04, Economics and Econometrics Research Institute (EERI), Brussels.
- 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.
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 references are entirely missing, you can add them using this form.