Rank Test Based On Matrix Perturbation Theory

Zaka Ratsimalahelo
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Zaka Ratsimalahelo: University of Franche-Comté

Econometrics from University Library of Munich, Germany

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).

Keywords: Rank Testing; Matrix Perturbation Theory; Rank Estimation; Singular Value Decomposition; Sequential Testing Procedure; Information Theoretic Criterion. (search for similar items in EconPapers)
JEL-codes: C12 C13 C30 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2003-06-20
New Economics Papers: this item is included in nep-ecm
Note: Type of Document - Acrobat PDF; prepared on PC, Scientific- Workplace; to print on HP/PostScript/; pages: 39 ; figures: included
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpem:0306008

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