Asymptotic Normality of Chatterjee's Rank Correlation
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908365932724224 |
|---|---|
| author | Kroll, Marius |
| author_facet | Kroll, Marius |
| contents | We prove that a suitably de-biased version of Chatterjee's rank correlation based on i.i.d. copies of a random vector $(X,Y)$ is asymptotically normal whenever $Y$ is not almost surely constant. No further conditions on the joint distribution of $X$ and $Y$ are required. We establish several results which allow us to extend convergence of the empirical process from one function class to larger function classes. These results are of independent interest, and can be used to investigate $V$-statistics and $V$-processes -- or, closely related, $U$-statistics and $U$-processes -- with dependent sample data. As an example, we use these results to prove weak convergence of $V$- and $U$-processes based on strongly mixing data. This implies a new limit theorem for $V$- and $U$-statistics of strongly mixing data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11547 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic Normality of Chatterjee's Rank Correlation Kroll, Marius Probability Statistics Theory 62H20, 60F05, 62G20, 62G30 We prove that a suitably de-biased version of Chatterjee's rank correlation based on i.i.d. copies of a random vector $(X,Y)$ is asymptotically normal whenever $Y$ is not almost surely constant. No further conditions on the joint distribution of $X$ and $Y$ are required. We establish several results which allow us to extend convergence of the empirical process from one function class to larger function classes. These results are of independent interest, and can be used to investigate $V$-statistics and $V$-processes -- or, closely related, $U$-statistics and $U$-processes -- with dependent sample data. As an example, we use these results to prove weak convergence of $V$- and $U$-processes based on strongly mixing data. This implies a new limit theorem for $V$- and $U$-statistics of strongly mixing data. |
| title | Asymptotic Normality of Chatterjee's Rank Correlation |
| topic | Probability Statistics Theory 62H20, 60F05, 62G20, 62G30 |
| url | https://arxiv.org/abs/2408.11547 |