Nonparametric estimation for derivatives of compound distribution

被引：1

作者：

Zhang, Zhimin ^{[1
]}

Liu, Chaolin ^{[1
]}

机构：

[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

来源：

JOURNAL OF THE KOREAN STATISTICAL SOCIETY | 2015年 / 44卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Compound; Fourier transform; Kernel; Asymptotic normality; Consistency; RENEWAL FUNCTION;

D O I：

10.1016/j.jkss.2014.09.006

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：

The compound random variable Sigma(N)(j=1) X-j and its distribution have many applications in actuarial science. In this paper, we consider estimation of the derivative functionals of the compound distribution when the underlying density f of X-j is unknown. The estimator is constructed by Fourier inversion and kernel method. An order bound for the bias and asymptotic expression for the variance are given, and the asymptotic normality and uniform consistency are also discussed. Some simulation studies are presented to illustrate the performance of the estimator under finite sample setting. (C) 2014 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

引用

页码：327 / 341

页数：15