Abstract
We study the problem of distributional approximations to high-dimensional non-degenerate U-statistics with random kernels of diverging orders. Infinite-order U-statistics (IOUS) are a useful tool for constructing simultaneous prediction intervals that quantify the uncertainty of ensemble methods such as subbagging and random forests. A major obstacle in using the IOUS is their computational intractability when the sample size and/or order are large. In this article, we derive non-asymptotic Gaussian approximation error bounds for an incomplete version of the IOUS with a random kernel. We also study data-driven inferential methods for the incomplete IOUS via bootstraps and develop their statistical and computational guarantees.
Original language | English (US) |
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Pages (from-to) | 4794-4848 |
Number of pages | 55 |
Journal | Electronic Journal of Statistics |
Volume | 13 |
Issue number | 2 |
DOIs | |
State | Published - 2019 |
Keywords
- Bootstrap
- Gaussian approximation
- Incomplete U statistics
- Infinite-order U-statistics
- Random forests
- Uncertainty quantification
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty