Drift estimation on non compact support for diffusion models

Fabienne Comte and Valentine Genon-Catalot

Stochastic Processes and their Applications, 2021, vol. 134, issue C, 174-207

Abstract: We study non parametric drift estimation for an ergodic diffusion process from discrete observations. The drift is estimated on a set A using an approximate regression equation by a least squares contrast, minimized over finite dimensional subspaces of L2(A,dx). The novelty is that the set A is non compact and the diffusion coefficient unbounded. Risk bounds of a L2-risk are provided where new variance terms are exhibited. A data-driven selection procedure is proposed where the dimension of the projection space is chosen within a random set contrary to usual selection procedures.

Keywords: Discrete time observation; Mean square estimator; Model selection; Nonparametric drift estimation; Stochastic differential equations (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2021.01.001

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