Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/142479
Authors: 
Ratsimalahelo, Zaka
Year of Publication: 
2001
Series/Report no.: 
EERI Research Paper Series 04/2001
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).
Subjects: 
Rank Testing Matrix Perturbation Theory Rank Estimation Singular Value Decomposition Sequential Testing Procedure Information Theoretic Criterion
JEL: 
C12
C13
C30
Document Type: 
Working Paper

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.