One-way or two-way factor model for matrix sequences?
One-way or two-way factor model for matrix sequences?
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DOI：
10.1016/j.jeconom.2023.02.008
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发表时间：
2021-10
影响因子：
6.3
通讯作者：
Yong He;Xinbing Kong;Lorenzo Trapani;Long Yu
中科院分区：
文献类型：
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作者：
Yong He;Xinbing Kong;Lorenzo Trapani;Long Yu
本文研究了矩阵值数据中行因子空间和列因子空间维数的确定问题。利用数据的样本秒矩矩阵频谱中的特征间隙，我们提出了一系列随机检验来检查是否存在单向或双向因素结构。我们的测试不需要任何特征值的任意阈值，并且可以（实际上）不限制横截面与样本量的相对发散率，因为它们趋于无穷大。虽然测试是基于随机化的，它不会逐渐消失，但我们提出了一个去随机化的“强”（基于迭代对数定律）决策规则来选择支持或反对共同因素的存在。我们以两种方式使用所提出的测试和决策规则。我们进一步将我们的单个测试投射到一个顺序过程中，该过程的输出是对公共因子数量的估计。我们的测试建立在数据的样本秒矩矩阵的两个变体上：一个基于矩阵值序列的行（或列）“扁平”版本，另一个基于基于投影的方法。我们的模拟表明，这两种方法在大样本中都能很好地工作，而在小样本中，基于投影方法的方法在几乎所有考虑的情况下都比现有方法提供了更好的性能。
This paper investigates the issue of determining the dimensions of row and column factor spaces in matrix-valued data. Exploiting the eigen-gap in the spectrum of sample second moment matrices of the data, we propose a family of randomised tests to check whether a one-way or two-way factor structure exists or not. Our tests do not require any arbitrary thresholding on the eigenvalues, and can be applied with (virtually) no restrictions on the relative rate of divergence of the cross-sections to the sample sizes as they pass to infinity. Although tests are based on a randomisation which does not vanish asymptotically, we propose a de-randomised, “strong” (based on the Law of the Iterated Logarithm) decision rule to choose in favour or against the presence of common factors. We use the proposed tests and decision rule in two ways. We further cast our individual tests in a sequential procedure whose output is an estimate of the number of common factors. Our tests are built on two variants of the sample second moment matrix of the data: one based on a row (or column) “flattened” version of the matrix-valued sequence, and one based on a projection-based method. Our simulations show that both procedures work well in large samples and, in small samples, the one based on the projection method delivers a superior performance compared to existing methods in virtually all cases considered.