• Bernoulli
  • Volume 24, Number 4A (2018), 2640-2675.

Gaussian approximation for high dimensional vector under physical dependence

Xianyang Zhang and Guang Cheng

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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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Bernoulli, Volume 24, Number 4A (2018), 2640-2675.

Received: January 2016
Revised: September 2016
First available in Project Euclid: 26 March 2018

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Zentralblatt MATH identifier

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


Zhang, Xianyang; Cheng, Guang. Gaussian approximation for high dimensional vector under physical dependence. Bernoulli 24 (2018), no. 4A, 2640--2675. doi:10.3150/17-BEJ939.

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