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
- 对矩阵值序列，如何判断行与列方向是否存在共同因子，并确定因子空间维度，同时避免人为设置特征值阈值？
- 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，结合迭代对数律决策规则，并通过序贯检验估计因子数量。
- 材料陈述的贡献
- 摘要称检验无需任意特征值阈值，也不限制横截面与样本量的相对发散速度；模拟中投影方法在小样本表现较好。
- 阅读关注点
- 应核对因子强度与依赖条件、单向和双向结构的检验定义、去随机化规则，以及序贯选择中的误判控制方式。
- 阅读边界
- 这是arXiv预印本，同行评审与期刊接收未核实；摘要未列完整正则条件，模拟优势仅适用于作者考察的情形。
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 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 randomization which does not vanish asymptotically, we propose a de-randomized, strong (based on the Law of the Iterated Logarithm) decision rule to choose in favor 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.