Nonparametric estimation of the trend in reflected fractional SDE

Marie, Nicolas

doi:10.1016/j.spl.2019.108659

Cited by 3 publications

(1 citation statement)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [37], Mishra and Prakasa Rao established the consistency and a rate of convergence of a nonparametric estimator of the whole trend of the solution to Equation (1) extending that of Kutoyants [31]. Marie [35] deals with the same estimator but for reflected fractional SDE. For nonparametric kernel-based estimators in Itô's calculus framework, the reader is referred to Kutoyants [31] and [32].…”

Section: Introductionmentioning

confidence: 99%

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

Comte¹,

Marie²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

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 Rsupported Hermite basis.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Comte¹,

Marie²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Nonparametric estimation for I.I.D. paths of fractional SDE

Comte

Marie

2021

Stat Inference Stoch Process

View full text Add to dashboard Cite

On a computable Skorokhod's integral‐based estimator of the drift parameter in fractional SDE

Marie

2024

Scandinavian J Statistics

View full text Add to dashboard Cite

This paper deals with a Skorokhod's integral‐based least squares‐ (LS) type estimator of the drift parameter computed from multiple (possibly dependent) copies of the solution of a stochastic differential equation (SDE) driven by a fractional Brownian motion of Hurst index . On the one hand, some convergence results are established on our LS estimator when . On the other hand, when , Skorokhod's integral‐based estimators cannot be computed from data, but in this paper some convergence results are established on a computable approximation of our LS estimator.

show abstract

Nonparametric estimation of the trend in reflected fractional SDE

Abstract: This paper deals with the consistency, a rate of convergence and the asymptotic distribution of a nonparametric estimator of the trend in the Skorokhod reflection problem defined by a fractional SDE and a Moreau sweeping process.

Cited by 3 publications

References 21 publications

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

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

Nonparametric estimation for I.I.D. paths of fractional SDE

On a computable Skorokhod's integral‐based estimator of the drift parameter in fractional SDE

Contact Info

Product

Resources

About