Nonparametric inference for fractional diffusion
arXiv:1111.0446 · doi:10.3150/13-BEJ509
Abstract
A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator based on the local approximation of the drift by a linear function. On the other hand, a Nadaraya-Watson kernel type estimator is studied. In both cases, some non-asymptotic results are proposed by means of deviation probability bound. The consistency property of the estimators are obtained under a one sided dissipative Lipschitz condition on the drift that insures the ergodic property for the stochastic differential equation. Our estimators are first constructed under continuous observations. The drift function is then estimated with discrete time observations that is of the most importance for practical applications.
Published in at http://dx.doi.org/10.3150/13-BEJ509 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
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- Nonparametric Estimation of the Trend in Reflected Fractional SDE
- On a Calculable Skorokhod's Integral Based Projection Estimator of the Drift Function in Fractional SDE
- Projection Estimators of the Stationary Density of a Differential Equation Driven by the Fractional Brownian Motion