Nonparametric estimation for compound Poisson process via variational analysis on measures
Journal article, 2018

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.

Compound Poisson distribution

Measure optimisation

Steepest descent algorithms

Gradient methods



Alexey Lindo

University of Glasgow

Sergey Zuev

Chalmers, Mathematical Sciences

University of Gothenburg

Mathematical Statistics

Serik Sagitov

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Statistics and Computing

0960-3174 (ISSN) 1573-1375 (eISSN)

Vol. 28 3 563-577

Subject Categories

Probability Theory and Statistics

Control Engineering

Signal Processing



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