Embracing the Blessing of Dimensionality in Factor Models
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：摘要研究一般高维因子模型的协方差估计，应用为微阵列数据，未明确涉及宏观因子或金融因子，故不作领域细分。
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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，加入目标集合之外的变量能否提高统计精度，其收益与计算成本如何衡量？
- 方法与思路
- 作者在高维因子模型中分析额外变量带来的信息增益与收敛率改善，并提出分治算法以减轻使用全部数据的计算负担。
- 材料陈述的贡献
- 摘要称，给出使用额外数据有益的充分条件，并量化信息与速率收益；变量足够多时可达类似因子已知的结果。
- 阅读关注点
- 应核对新增变量与共同因子的关系、达到类似已知因子表现的条件，以及分治算法不损失统计精度的具体比较标准。
- 阅读边界
- 所据为 arXiv 预印本，同行评审及期刊接收未核实；摘要未列出充分条件，不能推断任意新增变量都会改善估计。
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.