A kernel type nonparametric density estimator for decompounding

Details A kernel type nonparametric density estimator for decompounding A kernel type nonparametric density estimator for decompounding

2005-05-17

arxiv.org/abs/math/0505355v4

Bernoulli 2007, Vol. 13, No. 3, 672-694

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.3150/07-BEJ6091 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6091

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.

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