Density estimation for compound Poisson processes from discrete data

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Duval, Celine^1,2 

[1] CREST, Paris, France

[2] Univ Paris 09, CNRS UMR 7534, F-75775 Paris 16, France

关键词: Compound Poisson process;    Discretely observed random process;    Decompounding;    Wavelet density estimation;   

DOI  :  10.1016/j.spa.2013.06.006

来源: Elsevier

【 摘 要 】

In this article we investigate the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over [0, T]. We consider the case where the sampling rate Delta = Delta(T) -> 0 as T -> infinity. We propose an adaptive wavelet threshold density estimator and study its performance for L-p losses, p >= 1, over Besov spaces. The main novelty is that we achieve minimax rates of convergence for sampling rates Delta(T) that vanish slowly. The estimation procedure is based on the explicit inversion of the operator giving the law of the increments as a nonlinear transformation of the jump density. (c) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free