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Rank Test Based On Matrix Perturbation Theory

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  • Zaka Ratsimalahelo
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    Abstract

    In this paper, we propose methods of the determination of the rank of matrix. We consider a rank test for an unobserved matrix for which an estimate exists having normal asymptotic distribution of order N1/2 where N is the sample size. The test statistic is based on the smallest estimated singular values. Using Matrix Perturbation Theory, the smallest singular values of random matrix converge asymptotically to zero in the order O(N-1) and the corresponding left and right singular vectors converge asymptotically in the order O(N-1/2). Moreover, the asymptotic distribution of the test statistic is seen to be chi-squared. The test has advantages over standard tests in being easier to compute. Two approaches are be considered sequential testing strategy and information theoretic criterion. We establish a strongly consistent of the determination of the rank of matrix using both the two approaches. Some economic applications are discussed and simulation evidence is given for this test. Its performance is compared to that of the LDU rank tests of Gill and Lewbel (1992) and Cragg and Donald (1996).

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    File URL: http://www.eeri.eu/documents/wp/EERI_RP_2001_04.pdf
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    Bibliographic Info

    Paper provided by Economics and Econometrics Research Institute (EERI), Brussels in its series EERI Research Paper Series with number EERI_RP_2001_04.

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    Length: 38 pages
    Date of creation: Jul 2001
    Date of revision:
    Handle: RePEc:eei:rpaper:eeri_rp_2001_04

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    Related research

    Keywords: Rank Testing Matrix Perturbation Theory Rank Estimation Singular Value Decomposition Sequential Testing Procedure Information Theoretic Criterion;

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    1. McCall, B P & McCall, J J, 1987. "A Sequential Study of Migration and Job Search," Journal of Labor Economics, University of Chicago Press, vol. 5(4), pages 452-76, October.
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    6. George J. Borjas, 1994. "The Economics of Immigration," Journal of Economic Literature, American Economic Association, vol. 32(4), pages 1667-1717, December.
    7. Bauer, Thomas K. & Zimmermann, Klaus F., 1999. "Report No. 3: Assessment of Possible Migration Pressure and its Labour Market Impact Following EU Enlargement to Central and Eastern Europe," IZA Research Reports 3, Institute for the Study of Labor (IZA).
    8. Carrington, William J & Detragiache, Enrica & Vishwanath, Tara, 1996. "Migration with Endogenous Moving Costs," American Economic Review, American Economic Association, vol. 86(4), pages 909-30, September.
    9. Hans-Werner Sinn & Gebhard Flaig & Martin Werding & Sonja Munz & Nicola Düll & Herbert Hofmann, 2001. "EU-Erweiterung und Arbeitskräftemigration : Wege zu einer schrittweisen Annäherung der Arbeitsmärkte," ifo Beiträge zur Wirtschaftsforschung, Ifo Institute for Economic Research at the University of Munich, number 2, March.
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    Cited by:
    1. D’Artis Kancs, 2005. "Can we use NEG models to predict migration flows? An example of CEE accession countries," Migration Letters, Migration Letters and The London Publishers, London, UK, vol. 2(1), pages 32-63, April.

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