In this paper we develop inference for high dimensional linear models, with serially correlated errors. We examine Lasso under the assumption of strong mixing in the covariates and error process, allowing for fatter tails in their distribution. While the Lasso estimator performs poorly under such circumstances, we estimate via GLS Lasso the parameters of interest and extend the asymptotic properties of the Lasso under more general conditions. Our theoretical results indicate that the non-asymptotic bounds for stationary dependent processes are sharper, while the rate of Lasso under general conditions appears slower as $T,p\to \infty$. Further we employ the debiased Lasso to perform inference uniformly on the parameters of interest. Monte Carlo results support the proposed estimator, as it has significant efficiency gains over traditional methods.
翻译:在本文中,我们开发了高维线性模型关于串行相关误差的推断。我们研究了Lasso的情况,假设协变量和误差过程之间具有强混合性,并允许它们的分布有更胖的尾巴。虽然在这种情况下Lasso估计量表现不佳,我们通过GLS Lasso估计感兴趣的参数,并在更一般的条件下扩展了Lasso的渐近性质。我们的理论结果表明,对于平稳依赖过程来说,非渐近界限更为精确,而在一般条件下,Lasso的速率看起来较慢,当$T,p\to \infty$时。此外,我们使用去偏Lasso来统一地推断出感兴趣的参数。蒙特卡罗结果支持了所提出的估计器,因为它具有显著的效率优势,可以比传统方法更好地完成推断。