Alexander Giessing, Jianqing Fan
arXiv 23 Jun 2020 · Mathematics — Statistics Theory · 1 citations (OpenAlex)
arXiv:2006.13099 · PDF · DOI · OpenAlex · Extracted main text
This paper considers a new bootstrap procedure to estimate the distribution of high-dimensional $\ell_p$-statistics, i.e. the $\ell_p$-norms of the sum of $n$ independent $d$-dimensional random vectors with $d \gg n$ and $p \in [1, \infty]$. We provide a non-asymptotic characterization of the sampling distribution of $\ell_p$-statistics based on Gaussian approximation and show that the bootstrap procedure is consistent in the Kolmogorov-Smirnov distance under mild conditions on the covariance structure of the data. As an application of the general theory we propose a bootstrap hypothesis test for simultaneous inference on high-dimensional mean vectors. We establish its asymptotic correctness and consistency under high-dimensional alternatives, and discuss the power of the test as well as the size of associated confidence sets. We illustrate the bootstrap and testing procedure numerically on simulated data.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bentkus, V (2003) On the dependence of the Berry–Esseen bound on dimension | 0.941 | 6 | 3 | 83% |
| 2 | Bickel, P. J. and Levina, E (2008) Covariance regularization by thresholding | 0.874 | 6 | 4 | 67% |
| 3 | Bickel, P. J. and Levina, E (2008) Regularized estimation of large covariance matrices | 0.874 | 6 | 4 | 67% |
| 4 | Fan, J., Liao, Y., and Yao, J (2015) Power enhancement in high-dimensional cross-sectional tests self | 0.811 | 4 | 2 | 100% |
| 5 | Chernozhukov, V., Chetverikov, D., and Kato, K (2015) Comparison and anti-concentration bounds for maxima of gaussian random vectors | 0.794 | 6 | 3 | 50% |
| 6 | Chernozhukov, V., Chetverikov, D., and Kato, K (2013) Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors | 0.737 | 10 | 5 | 40% |
| 7 | Chernozhukov, V., Chetverikov, D., and Kato, K (2017) Central limit theorems and bootstrap in high dimensions | 0.737 | 10 | 4 | 40% |
| 8 | Götze, F., Naumov, A., Spokoiny, V., and Ulyanov, V (2019) Large ball probabilities, Gaussian comparison and anti-concentration | 0.737 | 4 | 3 | 50% |
| 9 | Schechtman, G. and Zinn, J (1990) On the volume of the intersection of two $l_p^n$ balls | 0.644 | 3 | 2 | 67% |
| 10 | Pouzo, D (2015) Bootstrap consistency for quadratic forms of sample averages with increasing dimension | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 56 scored citations.