Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.14428 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909794396274688 |
|---|---|
| author | Zou, Haolin Yao, Heyuan de la Peña, Victor |
| author_facet | Zou, Haolin Yao, Heyuan de la Peña, Victor |
| contents | Following the student t-statistic, normalization has been a widely used method in statistic and other disciplines including economics, ecology and machine learning. We focus on statistics taking the form of a ratio over (some power of) the sample mean, the probabilistic features of which remain unknown. We develop a unified formula for the moments of these self-normalized statistics with non-negative observations, yielding closed-form expressions for several important cases. Moreover, the complexity of our formula doesn't scale with the sample size $n$. Our theoretical findings, supported by extensive numerical experiments, reveal novel insights into their bias and variance, and we propose a debiasing method illustrated with applications such as the odds ratio, Gini coefficient and squared coefficient of variation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Scalable Formula for the Moments of a Family of Self-Normalized Statistics Zou, Haolin Yao, Heyuan de la Peña, Victor Statistics Theory Computation Following the student t-statistic, normalization has been a widely used method in statistic and other disciplines including economics, ecology and machine learning. We focus on statistics taking the form of a ratio over (some power of) the sample mean, the probabilistic features of which remain unknown. We develop a unified formula for the moments of these self-normalized statistics with non-negative observations, yielding closed-form expressions for several important cases. Moreover, the complexity of our formula doesn't scale with the sample size $n$. Our theoretical findings, supported by extensive numerical experiments, reveal novel insights into their bias and variance, and we propose a debiasing method illustrated with applications such as the odds ratio, Gini coefficient and squared coefficient of variation. |
| title | A Scalable Formula for the Moments of a Family of Self-Normalized Statistics |
| topic | Statistics Theory Computation |
| url | https://arxiv.org/abs/2509.14428 |