Embracing the Blessing of Dimensionality in Factor Models
充分利用因子模型中的维度优势AI 解读 ↓
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分类依据与纠错
AI 根据所提供的论文材料归类：摘要研究通用高维因子协方差估计并应用于基因数据，缺少宏观或金融因子方向的直接依据。
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充分利用因子模型中的维度优势
- 研究问题
- 估计一组目标变量的协方差矩阵时，加入目标之外的变量能否提高精度，增加信息的收益又如何衡量？
- 方法与思路
- 作者在高维因子模型中给出使用额外变量的充分条件，以 Fisher 信息和收敛率衡量收益，并提出分而治之算法。
- 材料陈述的贡献
- 摘要称，变量足够多时可达到类似已知因子的估计效果；分而治之不损失相对合并分析的统计精度，并有模拟与基因数据示例。
- 阅读关注点
- 应核对额外变量提供有效因子信息的条件、维度与样本量的关系，以及分而治之算法的划分规则和精度保证范围。
- 阅读边界
- 所给材料是 arXiv 1610.07697v1 预印本摘要，不能据此声称已同行评审或期刊接收；具体条件、收益大小及刊本变化未提供。
原文摘要
Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the blessing of dimensionality has not yet been fully embraced in the literature: much of the available data is often ignored in constructing covariance matrix estimates. If our goal is to accurately estimate a covariance matrix of a set of targeted variables, shall we employ additional data, which are beyond the variables of interest, in the estimation? In this paper, we provide sufficient conditions for an affirmative answer, and further quantify its gain in terms of Fisher information and convergence rate. In fact, even an oracle-like result (as if all the factors were known) can be achieved when a sufficiently large number of variables is used. The idea of utilizing data as much as possible brings computational challenges. A divide-and-conquer algorithm is thus proposed to alleviate the computational burden, and also shown not to sacrifice any statistical accuracy in comparison with a pooled analysis. Simulation studies further confirm our advocacy for the use of full data, and demonstrate the effectiveness of the above algorithm. Our proposal is applied to a microarray data example that shows empirical benefits of using more data.