Nonparametric Estimation for I.I.D. Paths of Fractional SDE
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2020
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917013677408256 |
|---|---|
| author | Comte, Fabienne Marie, Nicolas |
| author_facet | Comte, Fabienne Marie, Nicolas |
| contents | This paper deals with nonparametric estimators of the drift function $b$ computed from independent continuous observations, on a compact time interval, of the solution of a stochastic differential equation driven by the fractional Brownian motion (fSDE). First, a risk bound is established on a Skorokhod's integral based least squares oracle $\widehat b$ of $b$. Thanks to the relationship between the solution of the fSDE and its derivative with respect to the initial condition, a risk bound is deduced on a calculable approximation of $\widehat b$. Another bound is directly established on an estimator of $b'$ for comparison. The consistency and rates of convergence are established for these estimators in the case of the compactly supported trigonometric basis or the $\mathbb R$-supported Hermite basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_03417 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Nonparametric Estimation for I.I.D. Paths of Fractional SDE Comte, Fabienne Marie, Nicolas Statistics Theory This paper deals with nonparametric estimators of the drift function $b$ computed from independent continuous observations, on a compact time interval, of the solution of a stochastic differential equation driven by the fractional Brownian motion (fSDE). First, a risk bound is established on a Skorokhod's integral based least squares oracle $\widehat b$ of $b$. Thanks to the relationship between the solution of the fSDE and its derivative with respect to the initial condition, a risk bound is deduced on a calculable approximation of $\widehat b$. Another bound is directly established on an estimator of $b'$ for comparison. The consistency and rates of convergence are established for these estimators in the case of the compactly supported trigonometric basis or the $\mathbb R$-supported Hermite basis. |
| title | Nonparametric Estimation for I.I.D. Paths of Fractional SDE |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2004.03417 |