Sequential Gaussian approximation for nonstationary time series in high dimensions

2022/03/07 by Mies, Fabian, Steland, Ansgar · 3 citations
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2203.03237

Abstract

Gaussian couplings of partial sum processes are derived for the high-dimensional regime d=o(n^1/3). The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities depend explicitly on the dimension and on a measure of nonstationarity, and are thus also applicable to arrays of random vectors. To enable high-dimensional statistical inference, a feasible Gaussian approximation scheme is proposed. Applications to sequential testing and change-point detection are described.

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