Adaptive estimation of the stationary density  of discrete and continuous time mixing
processes

Fabienne Comte; Florence Merlevède

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Displaying similar documents to “Adaptive estimation of the stationary density of discrete and continuous time mixing processes”

Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process

Eva Löcherbach, Dasha Loukianova, Oleg Loukianov (2011)

ESAIM: Probability and Statistics

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Let be a one dimensional positive recurrent diffusion continuously observed on [0,] . We consider a non parametric estimator of the drift function on a given interval. Our estimator, obtained using a penalized least square approach, belongs to a finite dimensional functional space, whose dimension is selected according to the data. The non-asymptotic risk-bound reaches the minimax optimal rate of convergence when → ∞. The main point of our work is that we do not suppose the process...

Nonparametric inference for discretely sampled Lévy processes

Shota Gugushvili (2012)

Annales de l'I.H.P. Probabilités et statistiques

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Given a sample from a discretely observed Lévy process = ( )≥0 of the finite jump activity, the problem of nonparametric estimation of the Lévy density corresponding to the process is studied. An estimator of is proposed that is based on a suitable inversion of the Lévy–Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of over suitable classes of Lévy triplets. The corresponding lower bounds are also...

Nonparametric estimation of the derivatives of the stationary density for stationary processes

Emeline Schmisser (2013)

ESAIM: Probability and Statistics

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In this article, our aim is to estimate the successive derivatives of the stationary density of a strictly stationary and -mixing process (). This process is observed at discrete times = 0 . The sampling interval can be fixed or small. We use a penalized least-square approach to compute adaptive estimators. If the derivative belongs to the Besov space $B_{2, \infty}^{α}$ B 2 , ∞ α , then our estimator converges at rate (). Then we consider a diffusion...

Semiparametric deconvolution with unknown noise variance

Catherine Matias (2010)

ESAIM: Probability and Statistics

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This paper deals with semiparametric convolution models, where the noise sequence has a Gaussian centered distribution, with unknown variance. Non-parametric convolution models are concerned with the case of an entirely known distribution for the noise sequence, and they have been widely studied in the past decade. The main property of those models is the following one: the more regular the distribution of the noise is, the worst the rate of convergence for the estimation of the signal's...