Reference : Invariant density adaptive estimation for ergodic jump diffusion processes over aniso...
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Physical, chemical, mathematical & earth Sciences : Mathematics
Invariant density adaptive estimation for ergodic jump diffusion processes over anisotropic classes
Amorino, Chiara* mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Gloter, Arnaud* [Université d'Evry > Lamme]
* These authors have contributed equally to this work.
In press
Journal of Statistical Planning and Inference
Yes (verified by ORBilu)
[en] Adaptive bandwidth selection ; anisotropic density estimation ; ergodic diffusion with jumps
[en] We consider the solution of a multivariate stochastic differential equation with Levy-type jumps and with unique invariant probability measure with density μ. We assume that a continuous record of observations is available.
In the case without jumps, Reiss and Dalalyan [7] and Strauch [24] have found convergence rates of invariant density estimators, under respectively isotropic and anisotropic H ̈older smoothness constraints, which are considerably faster than those known from standard multivariate density estimation.
We extend the previous works by obtaining, in presence of jumps, some estimators which have the same convergence rates they had in the case without jumps for d ≥ 2 and a rate which depends on the degree of the jumps in the one-dimensional setting.
We propose moreover a data driven bandwidth selection procedure based on the Goldenshluger and Lepski method [11] which leads us to an adaptive non-parametric kernel estimator of the stationary density μ of the jump diffusion X.

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