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
相关论文
共 50 条
  • [1] Analysis of Nonparametric Kernel Density Estimator in OFDM Systems
    Vega-Lozada, Victor A.
    Lambertt Lobaina, Angel
    IMCIC 2010: INTERNATIONAL MULTI-CONFERENCE ON COMPLEXITY, INFORMATICS AND CYBERNETICS, VOL I (POST-CONFERENCE EDITION), 2010, : 53 - 56
  • [2] Nonparametric Probabilistic Unbalanced Power Flow With Adaptive Kernel Density Estimator
    Nosratabadi, Hossein
    Mohammadi, Mohammad
    Kargarian, Amin
    IEEE TRANSACTIONS ON SMART GRID, 2019, 10 (03) : 3292 - 3300
  • [3] New type of gamma kernel density estimator
    Rizky Reza Fauzi
    Yoshihiko Maesono
    Journal of the Korean Statistical Society, 2020, 49 : 882 - 900
  • [4] New type of gamma kernel density estimator
    Fauzi, Rizky Reza
    Maesono, Yoshihiko
    JOURNAL OF THE KOREAN STATISTICAL SOCIETY, 2020, 49 (03) : 882 - 900
  • [5] Robust nonparametric kernel regression estimator
    Zhao, Ge
    Ma, Yanyuan
    STATISTICS & PROBABILITY LETTERS, 2016, 116 : 72 - 79
  • [6] Weak and strong uniform consistency of a kernel error density estimator in nonparametric regression
    Cheng, FX
    JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2004, 119 (01) : 95 - 107
  • [7] Nonparametric multiplicative bias correction for von Mises kernel circular density estimator
    Bedouhene, Kahina
    Zougab, Nabil
    COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 2022, 51 (03) : 774 - 792
  • [8] Nonparametric log kernel estimator of extropy function
    Irshad, Muhammed Rasheed
    Maya, Radhakumari
    CHILEAN JOURNAL OF STATISTICS, 2022, 13 (02): : 155 - 163
  • [9] Nonparametric k-sample test based on kernel density estimator for paired design
    Martinez-Camblor, Pablo
    COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2010, 54 (08) : 2035 - 2045
  • [10] Decompounding random sums: a nonparametric approach
    Martin Bøgsted
    Susan M. Pitts
    Annals of the Institute of Statistical Mathematics, 2010, 62 : 855 - 872