Nonparametric estimation for I.I.D. paths of fractional SDE
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 Skorokh...
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| Veröffentlicht in: | Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems 2021-10, Vol.24 (3), p.669-705 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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
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
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
R
-supported Hermite basis. |
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| ISSN: | 1387-0874 1572-9311 |
| DOI: | 10.1007/s11203-021-09246-4 |