Asymptotic behaviour of the empirical distance covariance for dependent data
- We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any measure with finite first moments, provided that the samples form a strictly stationary and ergodic process. We further give a result concerning the asymptotic distribution of the empirical distance covariance under the assumption of absolute regularity of the samples and extend these results to certain types of pseudometric spaces. In the process, we derive a general theorem concerning the asymptotic distribution of degenerate V-statistics of order 2 under a strong mixing condition.
| Author: | Marius KrollORCiDGND |
|---|---|
| URN: | urn:nbn:de:hbz:294-96914 |
| DOI: | https://doi.org/10.1007/s10959-021-01073-w |
| Parent Title (English): | Journal of theoretical probability |
| Publisher: | Springer Science + Business Media B.V. |
| Place of publication: | New York |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2023/02/24 |
| Date of first Publication: | 2021/01/06 |
| Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
| Tag: | Distance correlation; Distance covariance; Mixing conditions; Negative type; Test of independence |
| Volume: | 35 |
| First Page: | 1226 |
| Last Page: | 1246 |
| Note: | Dieser Beitrag ist auf Grund des DEAL-Springer-Vertrages frei zugänglich. |
| Dewey Decimal Classification: | Naturwissenschaften und Mathematik / Mathematik |
| open_access (DINI-Set): | open_access |
| faculties: | Fakultät für Mathematik |
| Licence (English): |  Creative Commons - CC BY 4.0 - Attribution 4.0 International |
