Central limit theorems for high dimensional dependent data
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909216062570496 |
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| author | Chang, Jinyuan Chen, Xiaohui Wu, Mingcong |
| author_facet | Chang, Jinyuan Chen, Xiaohui Wu, Mingcong |
| contents | 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 ($α$-mixing, $m$-dependent, and physical dependence measure). In particular, we establish new error bounds under the $α$-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 estimator for the long-run covariance matrices. We apply the unified Gaussian and bootstrap approximation results to test mean vectors with combined $\ell^2$ and $\ell^\infty$ type statistics, change point detection, and construction of confidence regions for covariance and precision matrices, all for time series data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_12929 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Central limit theorems for high dimensional dependent data Chang, Jinyuan Chen, Xiaohui Wu, Mingcong Statistics Theory Probability 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 ($α$-mixing, $m$-dependent, and physical dependence measure). In particular, we establish new error bounds under the $α$-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 estimator for the long-run covariance matrices. We apply the unified Gaussian and bootstrap approximation results to test mean vectors with combined $\ell^2$ and $\ell^\infty$ type statistics, change point detection, and construction of confidence regions for covariance and precision matrices, all for time series data. |
| title | Central limit theorems for high dimensional dependent data |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2104.12929 |