Electronic Journal of Statistics

Adaptive procedure for Fourier estimators: application to deconvolution and decompounding

Céline Duval and Johanna Kappus

Full-text: Open access

Abstract

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 $\Delta$.

Article information

Source
Electron. J. Statist., Volume 13, Number 2 (2019), 3424-3452.

Dates
Received: April 2019
First available in Project Euclid: 25 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1569398615

Digital Object Identifier
doi:10.1214/19-EJS1602

Subjects
Primary: 62C12: Empirical decision procedures; empirical Bayes procedures 62C20: Minimax procedures
Secondary: 62G07: Density estimation

Keywords
Adaptive density estimation deconvolution decompounding model selection

Rights
Creative Commons Attribution 4.0 International License.

Citation

Duval, Céline; Kappus, Johanna. Adaptive procedure for Fourier estimators: application to deconvolution and decompounding. Electron. J. Statist. 13 (2019), no. 2, 3424--3452. doi:10.1214/19-EJS1602. https://projecteuclid.org/euclid.ejs/1569398615


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