Open Access
November 2018 Gaussian approximation for high dimensional vector under physical dependence
Xianyang Zhang, Guang Cheng
Bernoulli 24(4A): 2640-2675 (November 2018). DOI: 10.3150/17-BEJ939


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.


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Xianyang Zhang. Guang Cheng. "Gaussian approximation for high dimensional vector under physical dependence." Bernoulli 24 (4A) 2640 - 2675, November 2018.


Received: 1 January 2016; Revised: 1 September 2016; Published: November 2018
First available in Project Euclid: 26 March 2018

zbMATH: 06853260
MathSciNet: MR3779697
Digital Object Identifier: 10.3150/17-BEJ939

Keywords: Gaussian approximation , high dimensionality , physical dependence measure , Slepian interpolation , Stein’s method , time series

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 4A • November 2018
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