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Tests Of Rank

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Author Info
Robin, Jean-Marc
Smith, Richard J.

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Abstract

This paper considers tests for the rank of a matrix for which a root-T consistent estimator is available. However, in contrast to tests associated with the minimum chi-square and asymptotic least squares principles, the estimator s asymptotic variance matrix is not required to be either full or of known rank. Test statistics based on certain estimated characteristic roots are proposed whose limiting distributions are a weighted sum of independent chi-squared variables. These weights may be simply estimated, yielding convenient estimators for the limiting distributions of the proposed statistics. A sequential testing procedure is presented that yields a consistent estimator for the rank of a matrix. A simulation experiment is conducted comparing the characteristic root statistics advocated in this paper with statistics based on the Wald and asymptotic least squares principles.

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File URL: http://journals.cambridge.org/abstract_S0266466600162012
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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 16 (2000)
Issue (Month): 02 (April)
Pages: 151-175
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:16:y:2000:i:02:p:151-175_16

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  1. Clark, Andrew & Etilé, Fabrice & Postel-Vinay, Fabien & Senik, Claudia & Van der Straeten, Karine, 2004. "Heterogeneity in Reported Well-Being: Evidence from Twelve European Countries," IZA Discussion Papers 1339, Institute for the Study of Labor (IZA). [Downloadable!]
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  2. Richard Paap & Frank Kleibergen, 2004. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Society 2004 Australasian Meetings 195, Econometric Society. [Downloadable!]
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  3. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2003. "Nonparametric IV estimation of shape-invariant Engel curves," CeMMAP working papers CWP15/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  4. Hiroyuki Kasahara & Katsumi Shimotsu, 2007. "Nonparametric Identification and Estimation of Multivariate Mixtures," Working Papers 1153, Queen's University, Department of Economics. [Downloadable!]
  5. Paul J Devereux, 2006. "Small Sample Bias in Synthetic Cohort Models of Labor Supply," Working Papers 200606, School Of Economics, University College Dublin. [Downloadable!]
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  6. 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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  7. Richard Smith, 2005. "Weak instruments and empirical likelihood: a discussion of the papers by DWK Andrews and JH Stock and Y Kitamura," CeMMAP working papers CWP13/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  8. Inoue, Atsushi & Rossi, Barbara, 2008. "Which Structural Parameters Are "Structural"? Identifying the Sources of Instabilities in Economic Models," Working Papers 08-02, Duke University, Department of Economics. [Downloadable!]
  9. Stephen G. Donald & Natércia Fortuna & Vladas Pipiras, 2005. "On rank estimation in symmetric matrices: the case of indefinite matrix estimators," FEP Working Papers 167, Universidade do Porto, Faculdade de Economia do Porto. [Downloadable!]
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  10. Stephen G. Donald & Natércia Fortuna & Vladas Pipiras, 2005. "Local and global rank tests for multivariate varying-coefficient models," FEP Working Papers 196, Universidade do Porto, Faculdade de Economia do Porto. [Downloadable!]
  11. Kapetanios, George & Marcellino, Massimiliano, 2006. "Impulse Response Functions from Structural Dynamic Factor Models: A Monte Carlo Evaluation," CEPR Discussion Papers 5621, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  12. Giovanni Forchini, 2006. "Tests for Over-identifying Restrictions in Partially Identified Linear Structural Equations," Monash Econometrics and Business Statistics Working Papers 20/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  13. Aghion, Philippe & Meghir, Costas & Vandenbussche, Jérôme, 2005. "Growth, Distance to Frontier and Composition of Human Capital," CEPR Discussion Papers 4860, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  14. 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!]
  15. Anyck Dauphin & Abdel-Rahmen El Lahga & Bernard Fortin & Guy Lacroix, 2004. "Choix de consommation des ménages en présence de plusieurs décideurs," CIRANO Working Papers 2004s-63, CIRANO. [Downloadable!]
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  16. Jérôme Vandenbussche & Philippe Aghion & Costas Meghir, 2006. "Growth, distance to frontier and composition of human capital," Journal of Economic Growth, Springer, vol. 11(2), pages 97-127, June. [Downloadable!] (restricted)
  17. Stéphane Bonhomme & Jean-Marc Robin, 2008. "Consistent noisy independent component analysis," CeMMAP working papers CWP04/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  18. Jérôme Adda & Jean-Marc Robin, 2003. "Aggregation of Non Stationary Demand Systems," Contributions to Economic Analysis & Policy, Berkeley Electronic Press, vol. 2(1), pages 1032-1032. [Downloadable!] (restricted)
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