Non parametric estimation for fractional diffusion processes with random effects. Issue 4 (4th July 2019)

• Record Type: Journal Article
• Authors: El Omari, Mohamed; El Maroufy, Hamid; Fuchs, Christiane
• Is Part Of: Statistics. Volume 53:Issue 4(2019)
• Page Start: 753
• Page End: 769
• Publication Date: 2019-07-04
• Subjects: Random effects model -- fractional Brownian motion -- nonparametric estimation -- density estimator -- histogram estimator; 62G86 -- 60G22 -- 62G20; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2019.1581783
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: We propose a nonparametric estimation for a class of fractional stochastic differential equations (FSDE) with random effects. We precisely consider general linear fractional stochastic differential equations with drift depending on random effects and non-random diffusion. We build ordinary kernel estimators and histogram estimators and study their L p risk ( p = 1 or 2 ), when H > 1 / 2 . Asymptotic results are evaluated as both T = T ( N ) and N tend to infinity.