Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.06813 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909198110949376 |
|---|---|
| author | Zhang, Qingyang |
| author_facet | Zhang, Qingyang |
| contents | This study investigates the extension of distance variance, a validated spread metric for continuous and binary variables [Edelmann et al., 2020, Ann. Stat., 48(6)], to quantify the spread of general categorical variables. We provide both geometric and algebraic characterizations of distance variance, revealing its connections to some commonly used entropy measures, and the variance-covariance matrix of the one-hot encoded representation. However, we demonstrate that distance variance fails to satisfy the Schur-concavity axiom for categorical variables with more than two categories, leading to counterintuitive results. This limitation hinders its applicability as a universal measure of spread. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06813 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on distance variance for categorical variables Zhang, Qingyang Methodology Statistics Theory This study investigates the extension of distance variance, a validated spread metric for continuous and binary variables [Edelmann et al., 2020, Ann. Stat., 48(6)], to quantify the spread of general categorical variables. We provide both geometric and algebraic characterizations of distance variance, revealing its connections to some commonly used entropy measures, and the variance-covariance matrix of the one-hot encoded representation. However, we demonstrate that distance variance fails to satisfy the Schur-concavity axiom for categorical variables with more than two categories, leading to counterintuitive results. This limitation hinders its applicability as a universal measure of spread. |
| title | A note on distance variance for categorical variables |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2405.06813 |