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2019 Adaptive procedure for Fourier estimators: application to deconvolution and decompounding
Céline Duval, Johanna Kappus
Electron. J. Statist. 13(2): 3424-3452 (2019). DOI: 10.1214/19-EJS1602


The purpose of this paper is twofold. First, introduce a new adaptive procedure to select the optimal – up to a logarithmic factor – cutoff parameter for Fourier density estimators. Two inverse problems are considered: deconvolution and decompounding. Deconvolution is a typical inverse problem, for which our procedure is numerically simple and stable, a comparison is performed with penalized techniques. Moreover, the procedure and the proof of oracle bounds do not rely on any knowledge on the noise term. Second, for decompounding, i.e. non-parametric estimation of the jump density of a compound Poisson process from the observation of $n$ increments at timestep $\Delta$, build an unified adaptive estimator which is optimal – up to a logarithmic factor – regardless the behavior of $\Delta$.


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Céline Duval. Johanna Kappus. "Adaptive procedure for Fourier estimators: application to deconvolution and decompounding." Electron. J. Statist. 13 (2) 3424 - 3452, 2019.


Received: 1 April 2019; Published: 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07113722
MathSciNet: MR4010984
Digital Object Identifier: 10.1214/19-EJS1602

Primary: 62C12, 62C20
Secondary: 62G07


Vol.13 • No. 2 • 2019
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