Positive Definite Kernels and Random Sequences Connected to Polynomial Hypergroups
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909404146696192 |
|---|---|
| author | Hösel, Volker |
| author_facet | Hösel, Volker |
| contents | This work explores new classes of nonstationary stochastic sequences associated with polynomial hypergroups. Their covariance structures are analyzed through positive definite kernels and corresponding Hilbert spaces. Novel consistent estimators are introduced for deriving covariance structures from sequence realizations. A comprehensive prediction theory is developed, including a fast Levinson-type algorithm for efficiently calculating best linear predictors. Wiener-type theorems are established, enabling the detection of spectral measure atoms via generalized periodograms. Additional advancements, such as prediction with supplementary information, further enhance the scope of this study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16864 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positive Definite Kernels and Random Sequences Connected to Polynomial Hypergroups Hösel, Volker Functional Analysis Statistics Theory This work explores new classes of nonstationary stochastic sequences associated with polynomial hypergroups. Their covariance structures are analyzed through positive definite kernels and corresponding Hilbert spaces. Novel consistent estimators are introduced for deriving covariance structures from sequence realizations. A comprehensive prediction theory is developed, including a fast Levinson-type algorithm for efficiently calculating best linear predictors. Wiener-type theorems are established, enabling the detection of spectral measure atoms via generalized periodograms. Additional advancements, such as prediction with supplementary information, further enhance the scope of this study. |
| title | Positive Definite Kernels and Random Sequences Connected to Polynomial Hypergroups |
| topic | Functional Analysis Statistics Theory |
| url | https://arxiv.org/abs/2411.16864 |