High-Dimensional Data Bootstrap
Victor Chernozhukov, Denis Chetverikov, Kengo Kato, Yuta Koike
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.
Topics & Concepts
Consistency (knowledge bases)InferenceHigh dimensionalComputer sciencePostselectionIntersection (aeronautics)Key (lock)Limit (mathematics)Data miningMathematicsAlgorithmArtificial intelligenceGeographyPhysicsComputer securityQuantum mechanicsMathematical analysisCartographyQuantum entanglementQuantumStatistical Methods and InferenceMarkov Chains and Monte Carlo MethodsStatistical Methods and Bayesian Inference