论文标题
高维最小二乘
High Dimensional Generalised Penalised Least Squares
论文作者
论文摘要
在本文中，我们开发了高维线性模型的推断，并具有串行相关的误差。我们检查了在协变量和误差过程中强烈混合的假设下的套索，从而使尾巴的分布较高。尽管在这种情况下，Lasso估计器的性能较差，但我们通过GLS套索估算了感兴趣的参数，并在更一般的条件下扩展了LASSO的渐近性能。我们的理论结果表明，固定依赖过程的非反应界限更加清晰，而在一般条件下的套索速率看起来较慢，较慢，$ t，p \ to \ infty $。此外，我们采用了Debias Lasso对感兴趣的参数统一地进行推论。蒙特卡洛结果支持拟议的估计器，因为它比传统方法具有显着的效率提高。
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.
