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, 327u2013351] sensitivity to the ordering of the variables for the LDU rank statistic of Cragg and Donald [Journal of the American Statistical Association (1996), 91, 1301u20131309] and Gill and Lewbel [Journal of the American Statistical Association (1992), 87, 766u2013776] a limiting distribution that is not a standard chi-squared distribution for the rank statistic of Robin and Smith [Econometric Theory (2000), 16, 151u2013175] usage of numerical optimization for the objective function statistic of Cragg and Donald [Journal of Econometrics (1997), 76, 223u2013250] 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 Unpublished working paper, U.F.R. Science Economique, University de Franche-Comtue9]. In the non-stationary cointegration case, the limiting distribution of the new rank statistic is identical to that of the Johansen trace statistic.
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机译：我们提出了一种新颖的统计数据来测试矩阵的秩。等级统计克服了现有等级统计的不足，例如：用于Anderson的标准相关等级统计的Kronecker协方差矩阵[数学统计年鉴（1951），22，327 u2013351]对LDU等级变量排序的敏感性Cragg和Donald [美国统计协会杂志（1996），91，1301 u20131309]和Gill and Lewbel [美国统计协会杂志（1992），87，766 u2013776）的统计量不是Robin和Smith的秩统计量的标准卡方分布[Econometric Theory（2000），16，151 u2013175]将数值优化用于Cragg和Donald的目标函数统计量[Journal of Econometrics（1997），76，223 u2013250]，并忽略了Ratsimalahelo [2002，基于矩阵摄动理论的秩检验]对奇异值的非负限制。 U.F.R.未发表的工作文件科学技术大学，弗朗什-孔德大学]。在非平稳协整情况下，新秩统计量的极限分布与Johansen跟踪统计量的极限分布相同。
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