Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5097596 | Journal of Econometrics | 2006 | 30 Pages |
Abstract
We propose a novel statistic to test the rank of a matrix. The rank statistic overcomes deficiencies of existing rank statistics, like: a Kronecker covariance matrix for the canonical correlation rank statistic of Anderson [Annals of Mathematical Statistics (1951), 22, 327-351] sensitivity to the ordering of the variables for the LDU rank statistic of Cragg and Donald [Journal of the American Statistical Association (1996), 91, 1301-1309] and Gill and Lewbel [Journal of the American Statistical Association (1992), 87, 766-776] a limiting distribution that is not a standard chi-squared distribution for the rank statistic of Robin and Smith [Econometric Theory (2000), 16, 151-175] usage of numerical optimization for the objective function statistic of Cragg and Donald [Journal of Econometrics (1997), 76, 223-250] and ignoring the non-negativity restriction on the singular values in Ratsimalahelo [2002, Rank test based on matrix perturbation theory. Unpublished working paper, U.F.R. Science Economique, University de Franche-Comté]. In the non-stationary cointegration case, the limiting distribution of the new rank statistic is identical to that of the Johansen trace statistic.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Frank Kleibergen, Richard Paap,