Translator Disclaimer
December 2020 Nonparametric drift estimation for i.i.d. paths of stochastic differential equations
Fabienne Comte, Valentine Genon-Catalot
Ann. Statist. 48(6): 3336-3365 (December 2020). DOI: 10.1214/19-AOS1933

Abstract

We consider $N$ independent stochastic processes $(X_{i}(t),t\in [0,T])$, $i=1,\ldots ,N$, defined by a one-dimensional stochastic differential equation, which are continuously observed throughout a time interval $[0,T]$ where $T$ is fixed. We study nonparametric estimation of the drift function on a given subset $A$ of ${\mathbb{R}}$. Projection estimators are defined on finite dimensional subsets of ${\mathbb{L}}^{2}(A,dx)$. We stress that the set $A$ may be compact or not and the diffusion coefficient may be bounded or not. A data-driven procedure to select the dimension of the projection space is proposed where the dimension is chosen within a random collection of models. Upper bounds of risks are obtained, the assumptions are discussed and simulation experiments are reported.

Citation

Download Citation

Fabienne Comte. Valentine Genon-Catalot. "Nonparametric drift estimation for i.i.d. paths of stochastic differential equations." Ann. Statist. 48 (6) 3336 - 3365, December 2020. https://doi.org/10.1214/19-AOS1933

Information

Received: 1 March 2019; Revised: 1 September 2019; Published: December 2020
First available in Project Euclid: 11 December 2020

MathSciNet: MR4185811
Digital Object Identifier: 10.1214/19-AOS1933

Subjects:
Primary: 62G07, 62M05

Rights: Copyright © 2020 Institute of Mathematical Statistics

JOURNAL ARTICLE
30 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.48 • No. 6 • December 2020
Back to Top