A kernel type nonparametric density estimator for decompounding

被引:41
|
作者
Van Es, Bert [1 ]
Gugushvili, Shota [1 ]
Spreij, Peter [1 ]
机构
[1] Univ Amsterdam, Korteweg Vries Inst Mathemat, NL-1018 TV Amsterdam, Netherlands
关键词
asymptotic normality; consistency; decompounding; kernel estimation;
D O I
10.3150/07-BEJ6091
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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.
引用
收藏
页码:672 / 694
页数:23
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