基于惩罚最小二乘的一步组因子分析
One-step group factor analysis via penalized least squares
- Nanjing Audit University（南京审计大学）
- Shanghai University of Finance and Economics（上海财经大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出基于惩罚最小二乘的一步组因子分析方法，在平衡组面板情形下性能优于两步典型相关方法，经模拟和实际数据验证可有效识别全局因子与局部模式。
AI中文摘要：
本文重新探讨组因子分析问题，提出一种一步惩罚最小二乘方法，用于估计高维组因子模型中的因子载荷与因子，为传统两步主成分方法提供了不同的替代方案。该方法源于组因子结构与精心设计的识别条件之间的等价关系，利用这一见解，我们为惩罚最小二乘损失函数构建了巧妙的拉格朗日乘子公式。这种一步优化框架结合微调后的惩罚参数，可直接推导因子载荷、因子得分、公共成分与局部成分的中心极限定理及其收敛速率。理论表明，在平衡组面板情形下，我们的一步方法达到与两步聚合主成分方法相同的收敛速率，甚至相同的极限标准误，且比两步典型相关方法的极限标准误更小。大量模拟研究验证了该理论，将其应用于美国房价与沪深300（CSI300）周度收益率数据，证实该方法可识别全局因子与异质性局部模式。
英文摘要：
In this article, we revisit the problem of group factor analysis and propose a one-step penalized least squares method to estimate the factor loadings and factors in large-dimensional group factor models, offering a distinct alternative to the conventional two-step principal component approach. Our procedure originates from the equivalence between the group factor structure and the carefully tailored identification conditions. Leveraging this insight, we develop a tricky Lagrange multiplier formulation for a penalized least square loss function. This one-step optimization framework, combined with the fine-tuned penalty parameters, facilitates the direct derivation of central limit theorems for factor loadings, factor scores, common and local components, as well as the convergence rates for them. Our theory demonstrates that our one-step approach achieves the same rate as the two-step aggregated principal-component method and even the same limiting standard error in the balanced group panel case, but smaller limiting standard error than the two-step canonical correlation procedure. Extensive simulation studies justify the theory. Applications to U.S. house prices and CSI300 weekly returns confirm that our method identifies global factors and heterogeneous local patterns.
