NUCLEAR NORM REGULARIZED QUANTILE REGRESSION WITH INTERACTIVE FIXED EFFECTS
研究了大N大T条件分位数面板数据模型，提出核范数惩罚估计量，无需预估计交互固定效应个数，允许协变量个数随样本量增长，并给出估计量的误差界和一致估计量。
This paper studies large N and large T conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the interactive fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of) interactive fixed effects. It also allows the number of covariates to grow slowly with N and T . We derive an error bound on the estimator that holds uniformly in the quantile level. The order of the bound implies uniform consistency of the estimator and is nearly optimal for the low-rank component. Given the error bound, we also propose a consistent estimator of the number of interactive fixed effects at any quantile level. We demonstrate the performance of the estimator via Monte Carlo simulations.