Fan Jianqing, Lou Zhipeng, Yu Mengxin
Frederick L. Moore '18 Professor of Finance, Professor of Statistics, and Professor of Operations Research and Financial Engineering at the Princeton University.
Department of Operations Research and Financial Engineering, Princeton University.
J Am Stat Assoc. 2024;119(546):1076-1088. doi: 10.1080/01621459.2023.2169700. Epub 2023 Feb 14.
We propose the Factor Augmented (sparse linear) Regression Model (FARM) that not only admits both the latent factor regression and sparse linear regression as special cases but also bridges dimension reduction and sparse regression together. We provide theoretical guarantees for the estimation of our model under the existence of sub-Gaussian and heavy-tailed noises (with bounded (1 + ) -th moment, for all > 0) respectively. In addition, the existing works on supervised learning often assume the latent factor regression or sparse linear regression is the true underlying model without justifying its adequacy. To fill in such an important gap on high-dimensional inference, we also leverage our model as the alternative model to test the sufficiency of the latent factor regression and the sparse linear regression models. To accomplish these goals, we propose the Factor-Adjusted deBiased Test (FabTest) and a two-stage ANOVA type test respectively. We also conduct large-scale numerical experiments including both synthetic and FRED macroeconomics data to corroborate the theoretical properties of our methods. Numerical results illustrate the robustness and effectiveness of our model against latent factor regression and sparse linear regression models.
我们提出了因子增强（稀疏线性）回归模型（FARM），该模型不仅将潜在因子回归和稀疏线性回归作为特殊情况包含在内，还将降维和稀疏回归联系在一起。我们分别在次高斯噪声和重尾噪声（对于所有(\epsilon > 0)，具有有界的((1 + \epsilon))阶矩）存在的情况下，为模型估计提供了理论保证。此外，现有的监督学习研究通常假设潜在因子回归或稀疏线性回归是真正的基础模型，却未对其充分性进行论证。为了填补高维推断方面的这一重要空白，我们还将我们的模型用作替代模型，以检验潜在因子回归模型和稀疏线性回归模型的充分性。为实现这些目标，我们分别提出了因子调整去偏检验（FabTest）和两阶段方差分析类型检验。我们还进行了大规模数值实验，包括合成数据和FRED宏观经济数据，以证实我们方法的理论性质。数值结果说明了我们的模型相对于潜在因子回归模型和稀疏线性回归模型的稳健性和有效性。
