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

  • Donald, Stephen G.
  • Fortuna, Nat rcia
  • Pipiras, Vladas

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

Volume (Year): 23 (2007)
Issue (Month): 06 (December)
Pages: 1217-1232

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Handle: RePEc:cup:etheor:v:23:y:2007:i:06:p:1217-1232_07
Contact details of provider: Postal: Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK
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  1. 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.
  2. Donkers, A.C.D. & Schafgans, M., 2003. "A Derivative Based Estimator for Semiparametric Index Models," Discussion Paper 2003-22, Tilburg University, Center for Economic Research.
  3. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(02), pages 151-175, April.
  4. 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.
  5. Bura, Efstathia & Cook, R. Dennis, 2003. "Rank estimation in reduced-rank regression," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 159-176, October.
  6. repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
  7. 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.
  8. Fortuna, Natercia, 2008. "Local rank tests in a multivariate nonparametric relationship," Journal of Econometrics, Elsevier, vol. 142(1), pages 162-182, January.
  9. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," Econometrics 0307007, EconWPA.
  10. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
  11. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
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