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A kernel type nonparametric density estimator for decompounding. (English) Zbl 1129.62030
Summary: Given a sample from a discretely observed compound Poisson process, we consider estimation of the density of the jump sizes. We propose a kernel type nonparametric density estimator and study its asymptotic properties. An order bound for the bias and an asymptotic expansion of the variance of the estimator are given. Pointwise weak consistency and asymptotic normality are established. The results show that, asymptotically, the estimator behaves very much like an ordinary kernel estimator.

62G07 Density estimation
62M09 Non-Markovian processes: estimation
65C60 Computational problems in statistics (MSC2010)
62G20 Asymptotic properties of nonparametric inference
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