arXiv 21 Dec 2025 · Statistics — Methodology
arXiv:2512.18627 · PDF · DOI · OpenAlex · Extracted main text
Uniform confidence bands for functions are widely used in empirical analysis. A variety of simple implementation methods (most notably multiplier bootstrap) have been proposed and theoretically justified. However, an implementation over a literally continuous index set is generally computationally infeasible, and practitioners therefore compute the critical value by evaluating the statistic on a finite evaluation grid. This paper quantifies how fine the evaluation grid must be for a multiplier bootstrap procedure over finite grid points to deliver valid uniform confidence bands. We derive an explicit bound on the resulting coverage error that separates discretization effects from the intrinsic high-dimensional bootstrap approximation error on the grid. The bound yields a transparent workflow for choosing the grid size in practice, and we illustrate the implementation through an example of kernel density estimation.
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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 | Chernozhukov, Victor and Chetverikov, Denis and Kato, Kengo and Koik… (2022) Improved central limit theorem and bootstrap approximation in high dimensions | 1.000 | 11 | 3 | 100% |
| 2 | Chernozhukov, Victor and Chetverikov, Denis and Kato, Kengo (2014) Gaussian approximation of suprema of empirical processes | 0.737 | 3 | 2 | 100% |
| 3 | Imai, Shunsuke and Qin, Lei and Yanagi, Takahide (2025) Doubly Robust Uniform Confidence Bands for Group-Time Conditional Average Treatment Effects in Difference-in-Differences self | 0.644 | 2 | 2 | 100% |
| 4 | Kato, Kengo and Sasaki, Yuya (2018) Uniform confidence bands in deconvolution with unknown error distribution | 0.644 | 2 | 2 | 100% |
| 5 | Le Cam, Lucien (1986) Asymptotic Methods in Statistical Decision Theory | 0.511 | 2 | 1 | 100% |
| 6 | Chen, Xiaohui and Kato, Kengo (2020) Jackknife multiplier bootstrap: finite sample approximations to the $U$-process supremum with applications | 0.405 | 1 | 1 | 100% |
| 7 | Bickel, Peter J and Rosenblatt, Murray (1973) On some global measures of the deviations of density function estimates | 0.405 | 1 | 1 | 100% |
| 8 | Chernozhukov, Victor and Chetverikov, Denis and Kato, Kengo (2014) Anti-concentration and honest, adaptive confidence bands | 0.405 | 1 | 1 | 100% |
| 9 | Chernozhukov, Victor and Chetverikov, Denis and Kato, Kengo (2016) Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings | 0.405 | 1 | 1 | 100% |
| 10 | Chernozhukov, Victor and Chetverikov, Denis and Kato, Kengo and Koik… (2023) High-dimensional data bootstrap | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 17 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A Grid-Rate Condition for Valid Uniform Inference | 0.644 | 2 | 2 |