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Total variation distance for discretely observed Lévy processes: a Gaussian approximation of the small jumps
Alexandra Carpentier, Céline Duval, Ester Mariucci
It is common practice to treat small jumps of Lévy processes as Wiener noise and thus to approximate its marginals by a Gaussian distribution. However, results that allow to quanti…
An adaptive procedure for Fourier estimators: illustration to deconvolution and decompounding
Céline Duval, Johanna Kappus
We introduce a new procedure to select the optimal cutoff parameter for Fourier density estimators that leads to adaptive rate optimal estimators, up to a logarithmic factor. This…
Nonparametric adaptive estimation for grouped data
Céline Duval, Johanna Kappus
The aim of this paper is to estimate the density f of a random variable X when one has access to independent observations of the sum of K 2 independent copies of X. We provid…
Nonparametric estimation of a renewal reward process from discrete data
Celine Duval
We study the nonparametric estimation of the jump density of a renewal reward process from one discretely observed sample path over [0,T]. We consider the regime when the sampling…
Statistical inference across time scales
Céline Duval, Marc Hoffmann
We investigate statistical inference across time scales. We take as toy model the estimation of the intensity of a discretely observed compound Poisson process with symmetric Berno…