• Bernoulli
  • Volume 13, Number 3 (2007), 672-694.

A kernel type nonparametric density estimator for decompounding

Bert van Es, Shota Gugushvili, and Peter Spreij

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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.

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Bernoulli, Volume 13, Number 3 (2007), 672-694.

First available in Project Euclid: 7 August 2007

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asymptotic normality consistency decompounding kernel estimation


van Es, Bert; Gugushvili, Shota; Spreij, Peter. A kernel type nonparametric density estimator for decompounding. Bernoulli 13 (2007), no. 3, 672--694. doi:10.3150/07-BEJ6091.

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