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

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

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)

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Natércia Fortuna

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.

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

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

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Article
- Donald, Stephen G. & Fortuna, Nat rcia & Pipiras, Vladas, 2007. "On Rank Estimation In Symmetric Matrices: The Case Of Indefinite Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 23(06), pages 1217-1232, December. [Downloadable!]

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation

This paper has been announced in the following NEP Reports:

NEP-ALL-2005-02-20 (All new papers)
NEP-ECM-2005-02-20 (Econometrics)
NEP-ETS-2005-02-20 (Econometric Time Series)

References listed on IDEAS
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Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250. [Downloadable!] (restricted)
repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
Frank Kleibergen & Richard Paap, 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Tinbergen Institute Discussion Papers 03-003/4, Tinbergen Institute. [Downloadable!]
Other versions:
- Kleibergen, F.R. & Paap, R., 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Institute Report EI 2003-01 Revision_Date:, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
- F. Kleibergen & R. Paap, 2003. "Generalized reduced rank tests using the singular value decomposition," Econometric Institute Report 301, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
- Richard Paap & Frank Kleibergen, 2004. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Society 2004 Australasian Meetings 195, Econometric Society. [Downloadable!]
- 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. [Downloadable!] (restricted)
Bura, Efstathia & Cook, R. Dennis, 2003. "Rank estimation in reduced-rank regression," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 159-176, October. [Downloadable!] (restricted)
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. [Downloadable!]
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. [Downloadable!] (restricted)
Natércia Fortuna, 2004. "Local rank tests in a multivariate nonparametric relationship," FEP Working Papers 137, Universidade do Porto, Faculdade de Economia do Porto. [Downloadable!]
Other versions:
- Natercia Fortuna, 2004. "Local rank tests in a multivariate nonparametric relationship," Econometric Society 2004 North American Summer Meetings 446, Econometric Society. [Downloadable!]
- Fortuna, Natercia, 2008. "Local rank tests in a multivariate nonparametric relationship," Journal of Econometrics, Elsevier, vol. 142(1), pages 162-182, January. [Downloadable!] (restricted)
Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May. [Downloadable!] (restricted)
B. Donkers & M. Schafgans, 2003. "A derivative based estimator for semiparametric index," Econometric Institute Report 313, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
Robin, J.M. & Smith, R.J., 1995. "Tests of Rank," Cambridge Working Papers in Economics 9521, Faculty of Economics, University of Cambridge.
Other versions:
- Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(02), pages 151-175, April. [Downloadable!]
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.
Donkers, B. & Schafgans, M., 2003. "A derivative based estimator for semiparametric index models," Discussion Paper 22, Tilburg University, Center for Economic Research. [Downloadable!]
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). [Downloadable!]
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. [Downloadable!]
Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," Econometrics 0307007, EconWPA. [Downloadable!]
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.

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