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On Rank Estimation In Symmetric Matrices: The Case Of Indefinite Matrix Estimators

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Author Info
Donald, Stephen G.
Fortuna, Nat rcia
Pipiras, Vladas

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Abstract

In 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.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 23 (2007)
Issue (Month): 06 (December)
Pages: 1217-1232
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:cup:etheor:v:23:y:2007:i:06:p:1217-1232_07

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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.:
  1. 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)
  2. repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
  3. 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:
  4. 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)
  5. 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!]
  6. 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)
  7. Natércia Fortuna, 2004. "Local rank tests in a multivariate nonparametric relationship," FEP Working Papers 137, Universidade do Porto, Faculdade de Economia do Porto. [Downloadable!]
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  8. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May. [Downloadable!] (restricted)
  9. B. Donkers & M. Schafgans, 2003. "A derivative based estimator for semiparametric index," Econometric Institute Report 313, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
  10. 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!]
  11. 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.
  12. Donkers, B. & Schafgans, M., 2003. "A derivative based estimator for semiparametric index models," Discussion Paper 22, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  13. 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!]
  14. 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!]
  15. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," Econometrics 0307007, EconWPA. [Downloadable!]
  16. 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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