Inference for low-rank models
研究高维参数矩阵可近似为尖峰低秩矩阵时的线性模型推断方法，提出基于核范数惩罚和两次普通最小二乘回归的步骤，实现渐近正态推断并达到半参数效率界，适用于矩阵补全、因子模型、变系数模型和异质性处理效应等场景。
This paper studies inference in linear models with a high-dimensional parameter matrix that can be well approximated by a “spiked low-rank matrix.” A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero singular values that diverge to infinity. We show that this framework covers a broad class of models of latent variables, which can accommodate matrix completion problems, factor models, varying coefficient models and heterogeneous treatment effects. For inference, we apply a procedure that relies on an initial nuclear-norm penalized estimation step followed by two ordinary least squares regressions. We consider the framework of estimating incoherent eigenvectors and use a rotation argument to argue that the eigenspace estimation is asymptotically unbiased. Using this framework, we show that our procedure provides asymptotically normal inference and achieves the semiparametric efficiency bound. We illustrate our framework by providing low-level conditions for its application in a treatment effects context where treatment assignment might be strongly dependent.