A kernel type nonparametric density estimator for decompounding
By Bert Van Es, S. Gugushvili, Peter Spreij. 2005
77 citations recorded by the source corpus.
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. Keywords: asymptotic normality; consistency; decompounding; kernel estimation Full-text: Access by subscription (subscriber: Univ Biblio SZ (UVA))
View Paper: https://www.semanticscholar.org/paper/2b46f25d81c0a0ec622b3f072ca86cc696cb94e9
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Citations in the corpus
- Estimation for L\'{e}vy processes from high frequency data within a long time interval (2011, methodology): “For simplicity, we have implemented the estimators h̄m̄, p̄m̄ defined by (10)-(20) and (27)-(32).”
- Nonparametric estimation for L\'evy processes from low-frequency observations (2007, background): “In the special case of compound Poisson processes the problem of estimating the jump density is known as decompounding, see van Es, Gugushvili, and Spreij (2007), Gugushvili (2007) and the references therein.”