DeepAI AI Chat
Log In Sign Up

Nonparametric Estimation for I.I.D. Paths of Fractional SDE

by   Fabienne Comte, et al.
Université Paris Descartes
Paris Nanterre University

This paper deals with nonparametric projection estimators of the drift function computed from independent continuous observations, on a compact time interval, of the solution of a stochastic differential equation driven by the fractional Brownian motion. A projection least-squares estimator is defined and a L^2-type risk bound is proved for it. The consistency and rate of convergence are established for these estimators in the case of the compactly supported trigonometric basis or the R-supported Hermite basis.


page 1

page 2

page 3

page 4


Nonparametric Estimation of the Trend in Reflected Fractional SDE

This paper deals with the consistency, a rate of convergence and the asy...

On a Projection Estimator of the Regression Function Derivative

In this paper, we study the estimation of the derivative of a regression...

Nonparametric Estimation for SDE with Sparsely Sampled Paths: an FDA Perspective

We consider the problem of nonparametric estimation of the drift and dif...

On a Computable Skorokhod's Integral Based Estimator of the Drift Parameter in Fractional SDE

This paper deals with a Skorokhod's integral based least squares type es...

Convex Regression in Multidimensions: Suboptimality of Least Squares Estimators

The least squares estimator (LSE) is shown to be suboptimal in squared e...