Decompounding: an estimation problem for Poisson random sums

By Boris Buchmann, R. Grübel. 2003

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Inference for the limiting cluster size distribution of extreme values (2008, background): “This idea has been proposed recently in [5] and [6] where it is assumed that a sample of the compound Poisson distribution is observed (which is unfortunately not the case here).”
A kernel type nonparametric density estimator for decompounding (2005, methodology): “The problem of nonparametric estimation of the distribution function F in the case of both continuous and discrete laws was treated by Buchmann and Grübel [1].”
Mixed Poisson Distributions (2005, background): “Remedies of this fact as well as properties of this kind of estimate are reported in Buchmann & Grubel (2003).”
A Donsker Theorem for Lévy Measures (2012, methodology): “In this case the Lévy measure ν is a finite measure and by explicit inversion in the convolution algebra Buchmann and Grübel (2003) prove a central limit theorem with rate 1/ √ n for a plug-in estimator of N in an exponentially weighted supremum norm, assuming that the intensity of the process is…”
Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process (2008, background): “, Yn from a compound Poisson process Y = (Yt )t≥0, nonparametric estimators of the jump size distribution function F (see [13,14]) and its density f (see [15]) were proposed and their asymptotics were studied as n → ∞.”