TESTS OF RANK
研究了矩阵秩的检验方法，提出基于特征根的检验统计量，其极限分布是加权卡方分布，并给出权重估计和序贯检验程序，通过模拟与Wald和渐近最小二乘法比较。
This paper considers tests for the rank of a matrix for which a root- T consistent estimator is available. However, in contrast to tests associated with the minimum chi-square and asymptotic least squares principles, the estimator's asymptotic variance matrix is not required to be either full or of known rank. Test statistics based on certain estimated characteristic roots are proposed whose limiting distributions are a weighted sum of independent chi-squared variables. These weights may be simply estimated, yielding convenient estimators for the limiting distributions of the proposed statistics. A sequential testing procedure is presented that yields a consistent estimator for the rank of a matrix. A simulation experiment is conducted comparing the characteristic root statistics advocated in this paper with statistics based on the Wald and asymptotic least squares principles.