Strongly Consistent Determination of the Rank of Matrix

Zaka Ratsimalahelo
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Zaka Ratsimalahelo: University of Franche-Comté

Econometrics from University Library of Munich, Germany

Abstract: In this paper, we develop methods of the determination of the rank of random matrix. Using the matrix perturbation theory to construct or find a suitable bases of the kernel (null space) of the matrix and to determine the limiting distribution of the estimator of the smallest singular values. We propose a new rank test for an unobserved matrix for which a root-N-consistent estimator is available and construct a Wald- type test statistic (generalized Wald test). The test, based on matrix perturbation theory, enable to determine how many singular values of the estimated matrix are insignificantly different from zero and we fully characterise the asymptotic distribution of the generalized Wald statistic under the most general conditions. We show that it is chi- square distribution under the null. In particular case, when the asymptotic covariance matrix has a Kronecker product form, the test statistic is equivalent to likelihood ratio test statistic and to Multiplier Lagrange test statistic. Two approaches to be considered are sequential testing strategy and information theoretic criterion. We establish a strongly consistent of the determination of the rank of matrix using the two approaches.

Keywords: Rank Testing; Matrix Perturbation Theory; Rank Estimation; Subspace Methods; Singular Value Decomposition; Weighting Matrices; Sequential Testing Strategy; Information Theoretic Criterion. (search for similar items in EconPapers)
JEL-codes: C1 C12 C13 C30 C5 C8 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2003-07-31
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: 36 ; figures: included
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpem:0307007

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