Wasserstein and Convex Gaussian Approximations for Non-stationary Time Series of Diverging Dimensionality
维度增长的非平稳时间序列的 Wasserstein 与凸集高斯逼近
In high-dimensional time series analysis, Gaussian approximation (GA) schemes under various distance measures or on various collections of subsets of the Euclidean space play a fundamental role in a wide range of statistical inference problems. To date, most GA results for high-dimensional time series are established on hyper-rectangles and their equivalence. In this paper, by considering the 2-Wasserstein distance and the collection of all convex sets, we establish a…