One-way or two-way factor model for matrix sequences?
矩阵序列应采用单向还是双向因子模型？AI 解读 ↓
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矩阵序列应采用单向还是双向因子模型？
- 研究问题
- 对于矩阵值数据，如何判断是否存在行或列公共因子，并确定两个因子空间的维数，而不依赖人为设置的特征值阈值？
- 方法与思路
- 作者利用样本二阶矩阵的特征值间隙构造随机化检验，再以迭代对数律形成去随机化决策规则，并通过序贯检验估计因子数。
- 材料陈述的贡献
- 摘要称，方法允许较宽松的横截面与样本量相对增长关系；所考察的小样本模拟中，投影方案在几乎所有情形下优于既有方法。
- 阅读关注点
- 应核对因子强度和依赖条件、随机化次数与决策规则，以及展开和投影两种矩阵构造对因子数判断的影响。
- 阅读边界
- 仅依据所给出版社摘要；增长率限制的例外、检验假设及模拟比较范围未具体说明，所述优势不能推广到未考察的数据结构。
原文摘要
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.