Computable Bounds for Strong Approximations with Applications
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916021697249280 |
|---|---|
| author | Ye, Haoyu Austern, Morgane |
| author_facet | Ye, Haoyu Austern, Morgane |
| contents | The Komlós$\unicode{x2013}$Major$\unicode{x2013}$Tusnády (KMT) inequality for partial sums is one of the most celebrated results in probability theory. Yet its practical application has been hindered by a lack of practical constants. This paper addresses this limitation for bounded i.i.d. random variables. At the cost of an additional logarithmic factor, we propose a computable version of the KMT inequality that depends only on the variables' range and standard deviation. We also derive an empirical version of the inequality that achieves nominal coverage even when the standard deviation is unknown. We then demonstrate the practicality of our bounds through applications to online change point detection and first hitting time probabilities. As a byproduct of our analysis, we obtain a Cramér-type moderate deviation bound for normalized centered partial sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03833 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computable Bounds for Strong Approximations with Applications Ye, Haoyu Austern, Morgane Statistics Theory Probability The Komlós$\unicode{x2013}$Major$\unicode{x2013}$Tusnády (KMT) inequality for partial sums is one of the most celebrated results in probability theory. Yet its practical application has been hindered by a lack of practical constants. This paper addresses this limitation for bounded i.i.d. random variables. At the cost of an additional logarithmic factor, we propose a computable version of the KMT inequality that depends only on the variables' range and standard deviation. We also derive an empirical version of the inequality that achieves nominal coverage even when the standard deviation is unknown. We then demonstrate the practicality of our bounds through applications to online change point detection and first hitting time probabilities. As a byproduct of our analysis, we obtain a Cramér-type moderate deviation bound for normalized centered partial sums. |
| title | Computable Bounds for Strong Approximations with Applications |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2508.03833 |