{"id":2544,"date":"2024-11-24T15:00:36","date_gmt":"2024-11-24T07:00:36","guid":{"rendered":"https:\/\/changjinyuan.com\/?p=2544"},"modified":"2024-12-28T22:31:36","modified_gmt":"2024-12-28T14:31:36","slug":"%e5%b8%b8%e6%99%8b%e6%ba%90-chen-x-%e5%90%b4%e6%98%8e%e8%81%aa-2024-central-limit-theorems-for-high-dimensional-dependent-data-bernoulli-30-712-742","status":"publish","type":"post","link":"https:\/\/changjinyuan.com\/index.php\/publications\/publications-all\/2544\/","title":{"rendered":"\u5e38\u664b\u6e90, Chen, X., & \u5434\u660e\u806a. (2024). Central limit theorems for high dimensional dependent data. Bernoulli, 30, 712-742."},"content":{"rendered":"

Motivated by statistical inference problems in high-dimensional time series data analysis, we first 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 a Gaussian random vector over three different dependency frameworks (\u03b1-mixing, m-dependent, and physical dependence measure). In particular, we establish new error bounds under the \u03b1-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. The unified Gaussian and parametric bootstrap approximation results can be used to test mean vectors with combined l2 and l\u221e type statistics, do change point detection, and construct confidence regions for covariance and precision matrices, all for time series data.<\/p>\r\n\r\n