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Gaussian approximation for high dimensional vector under physical dependence. (English) Zbl 1419.62257

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 V. Chernozhukov et al. [Ann. Stat. 41, No. 6, 2786–2819 (2013; Zbl 1292.62030)] to time series based on a variant of Stein’s method developed therein.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E17 Approximations to statistical distributions (nonasymptotic)
60F05 Central limit and other weak theorems

Citations:

Zbl 1292.62030
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Full Text: DOI Euclid

References:

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