Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/142494 
Year of Publication: 
2003
Series/Report no.: 
EERI Research Paper Series No. 4/2003
Publisher: 
Economics and Econometrics Research Institute (EERI), Brussels
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.
Subjects: 
Rank Testing
Matrix Perturbation Theory
Rank Estimation
Subspace Methods
Singular Value Decomposition
Weighting Matrices
Sequential Testing Strategy
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.