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

Florian Dussap (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

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.

Mots clés: nonparametric estimator; rate of estimation; classical risk model; Gerber-Shiu function; Laguerre series expansion; Fourier inversion

Domaines: Statistiques [math.ST]

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⟩