Rank Test Based On Matrix Perturbation Theory
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).
|Date of creation:||20 Jun 2003|
|Date of revision:|
|Note:||Type of Document - Acrobat PDF; prepared on PC, Scientific- Workplace; to print on HP/PostScript/; pages: 39 ; figures: included|
|Contact details of provider:|| Web page: http://econwpa.repec.org|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
- Donald W.K. Andrews, 1985.
"Asymptotic Results for Generalized Wald Tests,"
Cowles Foundation Discussion Papers
761R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1986.
- Sin, Chor-Yiu & White, Halbert, 1996. "Information criteria for selecting possibly misspecified parametric models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 207-225.
- Lwebel Arthur & Perraudin William, 1995. "A Theorem on Portfolio Separation with General Preferences," Journal of Economic Theory, Elsevier, vol. 65(2), pages 624-626, April.
- Alastair R. Hall & Glenn D. Rudebusch & David W. Wilcox, 1994.
"Judging instrument relevance in instrumental variables estimation,"
Finance and Economics Discussion Series
94-3, Board of Governors of the Federal Reserve System (U.S.).
- Hall, Alastair R & Rudebusch, Glenn D & Wilcox, David W, 1996. "Judging Instrument Relevance in Instrumental Variables Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 283-98, May.
- Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
- Pötscher, B.M., 1991. "Effects of Model Selection on Inference," Econometric Theory, Cambridge University Press, vol. 7(02), pages 163-185, June.
- Zhao, L. C. & Krishnaiah, P. R. & Bai, Z. D., 1986. "On detection of the number of signals in presence of white noise," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 1-25, October.
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpem:0306008. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)
If references are entirely missing, you can add them using this form.