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Nonparametric estimation for compound Poisson process via variational analysis on measures

Journal article
Authors A. Lindo
Sergei Zuyev
Serik Sagitov
Published in Statistics and Computing
Volume 28
Issue 3
Pages 563-577
ISSN 0960-3174
Publication year 2018
Published at Department of Mathematical Sciences
Pages 563-577
Language en
Keywords Compound Poisson distribution, Decompounding, Measure optimisation, Gradient methods, density-estimation, levy processes, random sums, functionals, space, Computer Science, Mathematics
Subject categories Mathematics


The paper develops new methods of nonparametric estimation of a compound Poisson process. Our key estimator for the compounding (jump) measure is based on series decomposition of functionals of a measure and relies on the steepest descent technique. Our simulation studies for various examples of such measures demonstrate flexibility of our methods. They are particularly suited for discrete jump distributions, not necessarily concentrated on a grid nor on the positive or negative semi-axis. Our estimators also applicable for continuous jump distributions with an additional smoothing step.

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