Decompounding Poisson random sums: recursively truncated estimates in the discrete case

DOI10.1007/BF02506487zbMath1078.62020MaRDI QIDQ2581125

Boris Buchmann, Rudolf Grübel

Publication date: 13 January 2006

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

zbMATH Keywords

likelihoodconsistencydiscrete distributionslimit distributionsplug-in principlecompound distributionshorse kick data

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Non-Markovian processes: estimation (62M09) Point estimation (62F10)

Related Items (14)

Asymptotic distributions for the intervals estimators of the extremal index and the cluster-size probabilities ⋮ Nonparametric Bayesian inference for multidimensional compound Poisson processes ⋮ Nonparametric inference for discretely sampled Lévy processes ⋮ Decompounding random sums: a nonparametric approach ⋮ Nonparametric estimation for compound Poisson process via variational analysis on measures ⋮ Statistical inference across time scales ⋮ Weighted empirical processes in the nonparametric inference for Lévy processes ⋮ Maxentropic approach to decompound aggregate risk losses ⋮ A non-parametric Bayesian approach to decompounding from high frequency data ⋮ A kernel type nonparametric density estimator for decompounding ⋮ Efficient nonparametric inference for discretely observed compound Poisson processes ⋮ Inference for the limiting cluster size distribution of extreme values ⋮ Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process ⋮ Nonparametric estimation in random sum models

Cites Work

• Unnamed Item
• Decompounding: an estimation problem for Poisson random sums.
• Bortkiewicz's Data and the Law of Small Numbers
• On a New Class of "Contagious" Distributions, Applicable in Entomology and Bacteriology
• EXPERIMENTAL EVIDENCE CONCERNING CONTAGIOUS DISTRIBUTIONS IN ECOLOGY
• Convergence of stochastic processes

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