Simultaneous inference for high-dimensional non-Gaussian time series is always considered to be a challenging problem. Such tasks require not only robust estimation of the coefficients in the random process, but also deriving limiting distribution for a sum of dependent variables. In this paper, we propose a multiplier bootstrap procedure to conduct simultaneous inference for the transition coefficients in high-dimensional non-Gaussian vector autoregressive (VAR) models. This bootstrap-assisted procedure allows the dimension of the time series to grow exponentially fast in the number of observations. As a test statistic, a de-biased estimator is constructed for simultaneous inference. Unlike the traditional de-biased/de-sparsifying Lasso estimator, robust convex loss function and normalizing weight function are exploited to avoid any unfavorable behavior at the tail of the distribution. We develop Gaussian approximation theory for VAR model to derive the asymptotic distribution of the de-biased estimator and propose a multiplier bootstrap-assisted procedure to obtain critical values under very mild moment conditions on the innovations. As an important tool in the convergence analysis of various estimators, we establish a Bernstein-type probabilistic concentration inequality for bounded VAR models. Numerical experiments verify the validity and efficiency of the proposed method.
翻译:在本文中,我们提出一个倍增靴陷阱程序,对高维非高加索矢量自动递增模型的过渡系数同时进行推论。这个靴子陷阱辅助程序允许时间序列的尺寸在观测数量上迅速迅速增长。作为测试统计数据,为同时推断而构建了一个除偏移的估测器。与传统的去偏向/去分分配拉索估计器不同的是,我们提出一个倍增靴套件程序,用以同时推算一个参数。我们提议了一个与传统的去偏向/去分分配拉索估计器不同的是,一个稳健的同流体损失功能和使重量功能正常化不同的是,以避免在分布的尾部出现任何不易变的行为。我们为VAR模型开发高斯近比理论,以得出已降偏移的测量器的无干扰分布,并提议一个用于同时推算的振荡测算器测算器。与传统的去偏移/去偏移的拉索估器分布器分布法不同的分数分配分配分配方法不同,在重要的贝尔那模式下,为重要的不平等率模型进行关键的比级分析。