Gaussian approximation for high dimensional vector under physical dependence

We develop a Gaussian approximation result for the maximum of a sum of weakly dependent vectors, where the data dimension is allowed to be exponentially larger than sample size. Our result is established under the physical/functional dependence framework. This work can be viewed as a substantive ext...

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Bibliographic Details
Published in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2018-11, Vol.24 (4A), p.2640-2675
Main Authors: ZHANG, XIANYANG, CHENG, GUANG
Format: Article
Language:English
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Summary:We develop a Gaussian approximation result for the maximum of a sum of weakly dependent vectors, where the data dimension is allowed to be exponentially larger than sample size. Our result is established under the physical/functional dependence framework. This work can be viewed as a substantive extension of Chernozhukov et al. (Ann. Statist. 41 (2013) 2786–2819) to time series based on a variant of Stein's method developed therein.
ISSN:1350-7265
DOI:10.3150/17-bej939