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

来源：

BERNOULLI | 2007年 / 13卷 / 03期

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

页码：672 / 694

页数：23

共 19 条

[1] Decompounding Poisson random sums:: Recursively truncated estimates in the discrete case
Buchmann, B
Grübel, R
[J]. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2004, 56 (04) : 743 - 756
[2] Buchmann B, 2003, ANN STAT, V31, P1054
[3] Carr P., 1999, Journal of Computational Finance, V2, P61
[4] Chung KL., 1974, COURSE PROBABILITY T
[5] DEVROYE L, 1991, NATO ADV SCI I C-MAT, V335, P31
[6] Embrechts P., 1997, MODELING EXTREMAL EV
[7] FINKELESTEIN M, 1997, P AM MATH SOC, V127, P2773
[8] Gyorfi L., 1985, The L 1 View
[9] HANSEN MB, 2006, AALBORGR200620
[10] A CONSISTENT NONPARAMETRIC DENSITY ESTIMATOR FOR THE DECONVOLUTION PROBLEM
LIU, MC
TAYLOR, RL
[J]. CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, 1989, 17 (04): : 427 - 438

← 1 2 →