Concentration inequalities for high-dimensional linear processes with dependent innovations

2023/07/23 by Mendes, Eduardo Fonseca, Lopes, Fellipe · 1 citation
#62M10 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2307.12395

Abstract

We develop concentration inequalities for the l_∞ norm of vector linear processes with sub-Weibull, mixingale innovations. This inequality is used to obtain a concentration bound for the maximum entrywise norm of the lag-h autocovariance matrix of linear processes. We apply these inequalities to sparse estimation of large-dimensional VAR(p) systems and heterocedasticity and autocorrelation consistent (HAC) high-dimensional covariance estimation.

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