Abstract
We establish general upper bounds on the Kolmogorov distance between two probability distributions in terms of the distance between these distributions as measured with respect to the Wasserstein or smooth Wasserstein metrics. These bounds generalise existing results from the literature. To illustrate the broad applicability of our general bounds, we apply them to extract Kolmogorov distance bounds from multivariate normal, beta and variance-gamma approximations that have been established in the Stein's method literature.
Original language | English |
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Article number | 126985 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 522 |
Issue number | 1 |
Early online date | 4 Jan 2023 |
DOIs | |
Publication status | Published - 1 Jun 2023 |
Keywords
- Kolmogorov distance
- Wasserstein distance
- integral probability metric
- inequality
- approximation
- Stein's method