A kernel type nonparametric density estimator for decompounding
Statistics Theory
2007-09-14 v4 Statistics Theory
Abstract
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.
Cite
@article{arxiv.math/0505355,
title = {A kernel type nonparametric density estimator for decompounding},
author = {Bert van Es and Shota Gugushvili and Peter Spreij},
journal= {arXiv preprint arXiv:math/0505355},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.3150/07-BEJ6091 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)