This article reviews recent progress in high-dimensional bootstrap. We first review high-
dimensional central limit theorems for distributions of sample mean vectors over the …

Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional
random vectors Page 1 The Annals of Statistics 2013, Vol. 41, No. 6, 2786–2819 DOI …

We propose a two-sample test for the means of high-dimensional data when the data
dimension is much larger than the sample size. Hotelling's classical T 2 test does not work …

Classification using high-dimensional features arises frequently in many contemporary
statistical studies such as tumor classification using microarray or other high-throughput …

Deep learning has become increasingly popular in both supervised and unsupervised
machine learning thanks to its outstanding empirical performance. However, because of …

We propose tests for sphericity and identity of high-dimensional covariance matrices. The
tests are nonparametric without assuming a specific parametric distribution for the data …

We propose two tests for the equality of covariance matrices between two high-dimensional
populations. One test is on the whole variance–covariance matrices, and the other is on off …

We propose simultaneous tests for coefficients in high-dimensional linear regression models
with factorial designs. The proposed tests are designed for the “large p, small n” situations …

Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled
by a single grossly outlying observation. As argued in the seminal work of Peter Huber in …

Power and reproducibility are key to enabling refined scientific discoveries in contemporary
big data applications with general high-dimensional nonlinear models. In this article, we …