Bernoulli

  • 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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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.

Article information

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

Dates
First available in Project Euclid: 7 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1186503482

Digital Object Identifier
doi:10.3150/07-BEJ6091

Mathematical Reviews number (MathSciNet)
MR2348746

Zentralblatt MATH identifier
1129.62030

Keywords
asymptotic normality consistency decompounding kernel estimation

Citation

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. https://projecteuclid.org/euclid.bj/1186503482


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