Abstract
Under correlation-type conditions, we derive an upper bound of order (log n)/n for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration inequalities on high-dimensional Euclidean spheres. Applications are illustrated on the example of log-concave probability measures.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1202-1219 |
| Number of pages | 18 |
| Journal | Annals of Probability |
| Volume | 48 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Publisher Copyright:© Institute of Mathematical Statistics, 2020.
Keywords
- Normal approximation
- Sudakov's typical distributions