High-Dimensional Data Bootstrap

Abstract

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 rectangles, bootstrap consistency results in high dimensions, and key techniques used to establish those results. We then review selected applications of high-dimensional bootstrap: construction of simultaneous confidence sets for high-dimensional vector parameters, multiple hypothesis testing via step-down, postselection inference, intersection bounds for partially identified parameters, and inference on best policies in policy evaluation. Finally, we also comment on a couple of future research directions.

Validating and Extending Psychopathy Measurement Tools in Convenience Samples

“…This test does not assume a relationship between means (i.e., is neutral to covariance matrix structure) or normality of the population. Both tests are a variation of the high-dimensional 8 data bootstrap algorithms (Chernozhukov et al, 2023) for establishing a non-parametric sampling distribution and associated confidence intervals. While the current datasets are not high-dimensional, the promise of non-parametric properties of these methods are appropriate as the dimensionality and structure of the SRP scale is under investigation.…”