Slow rates of approximation of U-statistics and V-statistics by quadratic forms of Gaussians
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913396509638656 |
|---|---|
| author | Huang, Kevin Han Orbanz, Peter |
| author_facet | Huang, Kevin Han Orbanz, Peter |
| contents | We construct examples of degree-two U- and V-statistics of $n$ i.i.d.~heavy-tailed random vectors in $\mathbb{R}^{d(n)}$, whose $ν$-th moments exist for ${ν> 2}$, and provide tight bounds on the error of approximating both statistics by a quadratic form of Gaussians. In the case ${ν=3}$, the error of approximation is $Θ(n^{-1/12})$. The proof adapts a result of Huang, Austern and Orbanz [12] to U- and V-statistics. The lower bound for U-statistics is a simple example of the concept of variance domination used in [12]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12437 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Slow rates of approximation of U-statistics and V-statistics by quadratic forms of Gaussians Huang, Kevin Han Orbanz, Peter Statistics Theory Probability We construct examples of degree-two U- and V-statistics of $n$ i.i.d.~heavy-tailed random vectors in $\mathbb{R}^{d(n)}$, whose $ν$-th moments exist for ${ν> 2}$, and provide tight bounds on the error of approximating both statistics by a quadratic form of Gaussians. In the case ${ν=3}$, the error of approximation is $Θ(n^{-1/12})$. The proof adapts a result of Huang, Austern and Orbanz [12] to U- and V-statistics. The lower bound for U-statistics is a simple example of the concept of variance domination used in [12]. |
| title | Slow rates of approximation of U-statistics and V-statistics by quadratic forms of Gaussians |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2406.12437 |