Rank Test Based On Matrix Perturbation Theory
AbstractIn 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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Bibliographic InfoPaper provided by Economics and Econometrics Research Institute (EERI), Brussels in its series EERI Research Paper Series with number EERI_RP_2001_04.
Length: 38 pages
Date of creation: Jul 2001
Date of revision:
Rank Testing Matrix Perturbation Theory Rank Estimation Singular Value Decomposition Sequential Testing Procedure Information Theoretic Criterion;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
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- 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).
- M. C. Burda, 1995.
"Migration and the Option Value of Waiting,"
SFB 373 Discussion Papers
1995,58, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Ratna Sahay & Carlos A. VÃ©gh Gramont & Stanley Fischer, 1998.
"How Far is Eastern Europe from Brussels?,"
IMF Working Papers
98/53, International Monetary Fund.
- George J. Borjas, 1988.
"Self-Selection and the Earnings of Immigrants,"
NBER Working Papers
2248, National Bureau of Economic Research, Inc.
- repec:wop:humbsf:1995-58 is not listed on IDEAS
- 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, December.
- George J. Borjas, 1994. "The Economics of Immigration," Journal of Economic Literature, American Economic Association, vol. 32(4), pages 1667-1717, December.
- 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.
- 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.
- D’Artis Kancs, 2005. "Can we use NEG models to predict migration flows? An example of CEE accession countries," Migration Letters, Transnational Press London, UK, vol. 2(1), pages 32-63, April.
- d’Artis Kancs, 2005. "Can we use NEG models to predict migration flows? An example of CEE accession countries," EERI Research Paper Series EERI_RP_2005_01, Economics and Econometrics Research Institute (EERI), Brussels.
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