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Rank Test Based On Matrix Perturbation Theory

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  • Zaka Ratsimalahelo

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).

Suggested Citation

  • Zaka Ratsimalahelo, 2001. "Rank Test Based On Matrix Perturbation Theory," EERI Research Paper Series EERI_RP_2001_04, Economics and Econometrics Research Institute (EERI), Brussels.
    • Handle: RePEc:eei:rpaper:eeri_rp_2001_04
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    File URL: http://www.eeri.eu/documents/wp/EERI_RP_2001_04.pdf
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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, vol. 2(1), pages 32-63, April.

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    More about this item

    Keywords

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

    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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