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High-dimensional Data Bootstrap

Author

Listed:
  • 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 stepdown, post-selection 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.

Suggested Citation

  • Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Yuta Koike, 2022. "High-dimensional Data Bootstrap," Papers 2205.09691, arXiv.org.
    • Handle: RePEc:arx:papers:2205.09691
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    References listed on IDEAS

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    2. Philipp Bach & Victor Chernozhukov & Martin Spindler, 2018. "Valid Simultaneous Inference in High-Dimensional Settings (with the hdm package for R)," Papers 1809.04951, arXiv.org.
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    5. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Yuta Koike, 2019. "Improved Central Limit Theorem and bootstrap approximations in high dimensions," Papers 1912.10529, arXiv.org, revised May 2022.
    6. Chetverikov, Denis, 2018. "Adaptive Tests Of Conditional Moment Inequalities," Econometric Theory, Cambridge University Press, vol. 34(1), pages 186-227, February.
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    9. Romano, Joseph P. & Wolf, Michael, 2016. "Efficient computation of adjusted p-values for resampling-based stepdown multiple testing," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 38-40.
    10. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    11. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
    12. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
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    16. Jinyuan Chang & Wen Zhou & Wen-Xin Zhou & Lan Wang, 2017. "Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering," Biometrics, The International Biometric Society, vol. 73(1), pages 31-41, March.
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