Displaying similar documents to “Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process”

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

Eva Löcherbach, Dasha Loukianova, Oleg Loukianov (2012)

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 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 , ∞ α B 2 , ∞ α , then our estimator converges at rate (). Then we consider a diffusion...

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

Fabienne Comte, Florence Merlevède (2010)

ESAIM: Probability and Statistics

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In this paper, we study the problem of non parametric estimation of the stationary marginal density of an or a -mixing process, observed either in continuous time or in discrete time. We present an unified framework allowing to deal with many different cases. We consider a collection of finite dimensional linear regular spaces. We estimate using a projection estimator built on a data driven selected linear space among the collection. This data driven choice is performed the minimization...

Towards a universally consistent estimator of the Minkowski content

Antonio Cuevas, Ricardo Fraiman, László Györfi (2013)

ESAIM: Probability and Statistics

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We deal with a subject in the interplay between nonparametric statistics and geometric measure theory. The measure () of the boundary of a set  ⊂ ℝ (with  ≥ 2) can be formally defined, a simple limit, by the so-called Minkowski content. We study the estimation of () from a sample of random points inside and outside . The sample design assumes that, for each sample point, we know (without error) whether or not that point belongs to . Under this design we...