Motivated by statistical inference problems in high-dimensional time series analysis, we derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles, simple convex sets and sparsely convex sets. We investigate the quantitative effect of temporal dependence on the rates of convergence to normality over three different dependency frameworks ($\alpha$-mixing, $m$-dependent, and physical dependence measure). In particular, we establish new error bounds under the $\alpha$-mixing framework and derive faster rate over existing results under the physical dependence measure. To implement the proposed results in practical statistical inference problems, we also derive a data-driven parametric bootstrap procedure based on a kernel-type estimator for the long-run covariance matrices.

翻译：以高维时间序列分析中的统计推断问题为动力,我们得出高斯对高方高度依赖性随机矢量的近似值的非零误差界限,这些近似值来自超矩形、简单的锥形和稀有的锥形。我们调查三个不同的依赖框架(美元-正构件、美元-依赖度和物理依赖度)对正常程度的暂时依赖率的定量影响。特别是,我们根据美元-正构件框架建立了新的误差界限,并在物理依赖度测量下得出比现有结果更快的速率。为了在实际统计推论问题中落实拟议结果,我们还根据长期共变基体的内核型估测算器,制定了数据驱动的参数测列器程序。