A unifying theory of tests of rank
研究了矩阵秩检验的一般原理，证明检验统计量可视为零空间估计量的隐函数，并通过插入原则确定其渐近行为，简化了多种备择假设和误设下的渐近分析，阐明了现有检验间的关系，并提出了许多新检验。
The general principles underlying tests of matrix rank are investigated. It is demonstrated that statistics for such tests can be seen as implicit functions of null space estimators. In turn, the asymptotic behaviour of the null space estimators is shown to determine the asymptotic behaviour of the statistics through a plug-in principle. The theory simplifies the asymptotics under a variety of alternatives of empirical relevance as well as misspecification, clarifies the relationships between the various existing tests, makes use of important results in the numerical analysis literature, and motivates numerous new tests. A brief Monte Carlo study illustrates the results.