Nonparametric Estimation of the Expected Discounted Penalty Function in the Compound Poisson Model - Archive ouverte HAL
Article Dans Une Revue Electronic Journal of Statistics Année : 2022

Nonparametric Estimation of the Expected Discounted Penalty Function in the Compound Poisson Model

Florian Dussap

Résumé

We propose a nonparametric estimator of the expected discounted penalty function in the compound Poisson risk model. We use a projection estimator on the Laguerre basis and we compute the coefficients using Plancherel theorem. We provide an upper bound on the MISE of our estimator, and we show it achieves parametric rates of convergence on Sobolev--Laguerre spaces without needing a bias-variance compromise. Moreover, we compare our estimator with the Laguerre deconvolution method. We compute an upper bound of the MISE of the Laguerre deconvolution estimator and we compare it on Sobolev--Laguerre spaces with our estimator. Finally, we compare these estimators on simulated data.
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Dates et versions

hal-03212783 , version 1 (30-04-2021)
hal-03212783 , version 2 (17-01-2022)

Identifiants

Citer

Florian Dussap. Nonparametric Estimation of the Expected Discounted Penalty Function in the Compound Poisson Model. Electronic Journal of Statistics , 2022, 16 (1), pp.2124-2174. ⟨10.1214/22-EJS2003⟩. ⟨hal-03212783v2⟩
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