We introduce a random-perturbation-based rank estimator of the number of factors of a large-dimensional approximate factor model. An expansion of the rank estimator demonstrates that the random perturbation reduces the biases due to the persistence of the factor series and the dependence between the factor and error series. A central limit theorem for the rank estimator with convergence rate higher than root |$n$| gives a new hypothesis-testing procedure for both one-sided and two-sided alternatives. Simulation studies verify the performance of the test.

中文翻译：

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基于随机扰动的因子数量秩估计

我们介绍了一个基于随机扰动的大维近似因子模型中因子数量的秩估计器。秩估计器的扩展表明，由于因子序列的持续性以及因子与误差序列之间的依赖性，随机扰动减小了偏差。收敛速度高于根| $ n $ |的秩估计的中心极限定理。给出了针对单面和双面选择的新的假设检验程序。仿真研究验证了测试的性能。