A high-dimensional CLT in W2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

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High-dimensional econometrics and regularized GMM (2018, background): “Recently, [120] improves on the Bentskus condition in the case where Z1, .”
Stein’s method for normal approximation in Wasserstein distances with application to the multivariate central limit theorem (2019, methodology): “As this result is √ log n short of optimality in the one-dimensional case, it is conjectured in [17] that”
Quantitative Central Limit Theorems for Discrete Stochastic Processes (2019, background): “It is also essentially tight, as Proposition 1.2 of Zhai (2018) shows that the W2 (Sk, Z) is lower bounded by Ω (√ d/k ) .”
Multivariate approximations in Wasserstein distance by Stein’s method and Bismut’s formula (2018, background): “Moreover, his general result [4, Theorem 1] extended those in [35, 3], and improved the multidimensional bound in [41] by removing some boundedness assumption and an additional logn factor therein.”
High-dimensional central limit theorems by Stein’s method (2020, methodology): “Following the proof of Proposition 1.4 of Zhai (2018), these bounds on the L2 transportation distance can be used to deduce a bound on suph=1A:A∈R |Eh(W) − Eh(Z)|.”