论文标题
潜在因子回归和稀疏回归是否足够？
Are Latent Factor Regression and Sparse Regression Adequate?
论文作者
论文摘要
我们提出了因子增强的稀疏线性回归模型（FARM），该模型不仅涵盖了潜在因子回归和稀疏线性回归作为特殊情况，而且还涵盖了降低尺寸和稀疏回归。我们提供了理论保证，以估算我们的模型，分别是高斯和重尾噪声的存在（分别为所有x> 0）。此外，现有有关监督学习的作品通常假定潜在因素回归或稀疏线性回归是真正的基础模型，而无需证明其足够的合理性。为了填补如此重要的空白，我们还利用模型作为替代模型来测试潜在因子回归的充分性和稀疏的线性回归模型。为了实现这些目标，我们提出了因子调整后的脱偏测试（FABTEST）和两阶段的ANOVA类型测试。我们还进行了大规模的数值实验，包括合成和弗雷德宏观经济学数据，以证实我们方法的理论特性。数值结果说明了我们模型对潜在因子回归和稀疏线性回归模型的鲁棒性和有效性。
We propose the Factor Augmented sparse linear Regression Model (FARM) that not only encompasses 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+x)-th moment, for all x>0), respectively. In addition, the existing works on supervised learning often assume the latent factor regression or the sparse linear regression is the true underlying model without justifying its adequacy. To fill in such an important gap, 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 de-Biased 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.
