A kernel type nonparametric density estimator for decompounding
van Es, Bert ; Gugushvili, Shota ; Spreij, Peter
Bernoulli, Tome 13 (2007) no. 1, p. 672-694 / Harvested from Project Euclid
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Given a sample from a discretely observed compound Poisson process, we consider estimation of the density of the jump sizes. We propose a kernel type nonparametric density estimator and study its asymptotic properties. An order bound for the bias and an asymptotic expansion of the variance of the estimator are given. Pointwise weak consistency and asymptotic normality are established. The results show that, asymptotically, the estimator behaves very much like an ordinary kernel estimator.
Publié le : 2007-08-14
Classification:  asymptotic normality,  consistency,  decompounding,  kernel estimation 
@article{1186503482,
     author = {van Es, Bert and Gugushvili, Shota and Spreij, Peter},
     title = {A kernel type nonparametric density estimator for decompounding},
     journal = {Bernoulli},
     volume = {13},
     number = {1},
     year = {2007},
     pages = { 672-694},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1186503482}
}

van Es, Bert; Gugushvili, Shota; Spreij, Peter. A kernel type nonparametric density estimator for decompounding. Bernoulli, Tome 13 (2007) no. 1, pp.  672-694. http://gdmltest.u-ga.fr/item/1186503482/