A kernel type nonparametric density estimator for decompounding
نویسندگان
چکیده
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. Asymptotic expansions of the bias and variance of the estimator are given and pointwise weak consistency and asymptotic normality are established. We also derive the minimax convergence rate for the quadratic loss function. The results show that asymptotically the estimator behaves very much like an ordinary kernel estimator.
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