[2104.12929] Central limit theorem for high-dimensional dependent data

Download the PDF of the paper entitled Central Limit Theorem for High-Dimensional Dependent Data by Jinyuan Chang and two other authors.

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overview: Motivated by the problem of statistical inference in high-dimensional time-series data analysis, first, non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors of hyperrectangles, simple convex sets, and sparse convex sets derives We investigate the quantitative effects of time dependence on the speed of convergence to Gaussian random vectors in three different dependence frameworks ($\alpha$ mixture, $m$ dependence, and physical dependence measurement). In particular, we establish new error bounds under the $\alpha$-mixing framework and derive faster rates than existing results under physics-dependent measurements. To implement the proposed results into practical statistical inference problems, we also derive a data-driven parametric bootstrapping procedure based on the kernel estimator of the long-term covariance matrix. Applying unified Gaussian and bootstrap fitting results to test mean vectors combining $\ell^2$ and $\ell^\infty$ type statistics, detect change points, and find covariance and construct a confidence region for the precision matrix. series data.