Penalized nonparametric mean square estimation of the coefficients of diffusion processes

Abstract : We consider a one-dimensional diffusion process (Xt) which is observed at n + 1 discrete times with regular sampling interval ∆. Assuming that (Xt) is strictly stationary, we propose nonparametric estimators of the drift and diffusion coefficients obtained by a penalized least square approach. Our estimators belong to a finite dimensional function space whose dimension is selected by a data-driven method. We provide non asymptotic risk bounds for the estimators. When the sampling interval tends to zero while the number of observations and the length of the observation time interval tend to infinity, we show that our estimators reach the minimax optimal rates of convergence. Numerical results based on exact simulations of diffusion processes are given for several examples of models and enlight the qualities of our estimation algorithms
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Article dans une revue
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2007, 13 (2), pp.514-543
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Fabienne Comte, Valentine Genon-Catalot, Yves Rozenholc. Penalized nonparametric mean square estimation of the coefficients of diffusion processes. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2007, 13 (2), pp.514-543. <hal-00748947>

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