Factor-adjusted regularized model selection
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因子调整的正则化模型选择
- 研究问题
- 当高维稀疏回归的协变量高度相关，且数据存在横截面和序列依赖时，如何恢复真实模型并改善变量选择与样本外预测？
- 方法与思路
- 作者提出 FarmSelect，估计潜在因子和特有成分，并同时将二者用作预测变量，通过扩展表示将高度相关的选择问题转为弱相关问题。
- 材料陈述的贡献
- 摘要称在一定条件下获得模型选择一致性与最优收敛速度，数值研究展示选择和预测表现，并提供实现该方法的 R 软件包。
- 阅读关注点
- 应核对因子分解和稀疏性的具体条件、因子估计误差如何进入选择理论、正则化调节方式，以及弱相关情形下无额外代价的含义。
- 阅读边界
- 所给出版社摘要未列出所谓温和条件、最优速度的具体表达或预测改善幅度；其一般回归框架不能仅凭应用动机归入宏观或金融因子。
原文摘要
This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when the covariates are highly correlated. Motivated by econometric and financial studies, we consider the case where covariate dependence can be reduced through the factor model, and propose a consistency strategy named Factor-Adjusted Regularized Model Selection (FarmSelect). By learning the latent factors and idiosyncratic components and using both of them as predictors, FarmSelect transforms the problem from model selection with highly correlated covariates to that with weakly correlated ones via lifting. Model selection consistency, as well as optimal rates of convergence, are obtained under mild conditions. Numerical studies demonstrate the nice finite sample performance in terms of both model selection and out-of-sample prediction. Moreover, our method is flexible in the sense that it pays no price for weakly correlated and uncorrelated cases. Our method is applicable to a wide range of high dimensional sparse regression problems. An R-package FarmSelect is also provided for implementation.