Bootstrapping High-Dimensional Time Series
Xianyang Zhang, University of Missouri-Columbia
In this talk, we will focus on the problem of conducting inference for high dimensional weakly dependent time series. Motivated by the applications in modern high dimensional inference, we derive a Gaussian approximation result for the maximum of a sum of weakly dependent vectors using Stein’s method, where the dimension of the vectors is allowed to be exponentially larger than sample size. Building on the Gaussian approximation result, we propose a blockwise multiplier (Wild) bootstrap that is able to capture the dependence between and within the data vectors and thus provides high-quality distributional approximation to the distribution of the maximum of vector sum in the high dimensional context. The usefulness of the method is illustrated via numerical studies.