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

Emeline Schmisser — 2013

ESAIM: Probability and Statistics

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 with known diffusion...

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