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

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

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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Bibliographic Info

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

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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. Natercia Fortuna, 2004. "Local rank tests in a multivariate nonparametric relationship," Econometric Society 2004 North American Summer Meetings 446, Econometric Society.
  3. 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.
  4. 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.
  5. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
  6. 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.
  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. 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.
  9. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(02), pages 151-175, April.
  10. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," Econometrics 0307007, EconWPA.
  11. 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.
  12. repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
  13. 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.
  14. Bura, Efstathia & Cook, R. Dennis, 2003. "Rank estimation in reduced-rank regression," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 159-176, October.
  15. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
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Cited by:
  1. Majid M. Al-Sadoon, 2014. "A general theory of rank testing," Economics Working Papers 1411, Department of Economics and Business, Universitat Pompeu Fabra.
  2. Ahn, Seung C. & Perez, M. Fabricio, 2010. "GMM estimation of the number of latent factors: With application to international stock markets," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 783-802, September.
  3. Jin, Fei & Lee, Lung-fei, 2013. "Cox-type tests for competing spatial autoregressive models with spatial autoregressive disturbances," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 590-616.

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