Hawkes process and Edgeworth expansion with application to maximum likelihood estimator

被引：4
|
作者：
Goda, Masatoshi [1 ,2 ]
机构：
[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 1538914, Japan
[2] Japan Sci & Technol, CREST, Kawaguchi, Japan
来源：
STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES | 2021年 / 24卷 / 02期
基金：
日本科学技术振兴机构;
关键词：
Hawkes process; Inferential statistics; Edgeworth expansion; Asymptotic expansion; Maximum likelihood estimator;
D O I：
10.1007/s11203-021-09237-5
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：
We provide a rigorous mathematical foundation of the theory for the higher-order asymptotic behavior of the one-dimensional Hawkes process with an exponential kernel. As an important application, we give the second-order asymptotic distribution for the maximum likelihood estimator of the exponential Hawkes process.
引用
收藏
页码：277 / 325
页数：49
相关论文
共 50 条
  • [1] Hawkes process and Edgeworth expansion with application to maximum likelihood estimator
    Masatoshi Goda
    Statistical Inference for Stochastic Processes, 2021, 24 : 277 - 325
  • [2] EDGEWORTH EXPANSION FOR THE DISTRIBUTION OF THE MAXIMUM LIKELIHOOD ESTIMATE IN THE VASICEK MODEL
    Zhu, Qinwen
    Liu, Hui
    Sun, Chengfeng
    ANNALS OF FINANCIAL ECONOMICS, 2019, 14 (01)
  • [3] THE BOOTSTRAPPED MAXIMUM-LIKELIHOOD ESTIMATOR WITH AN APPLICATION
    BURKE, MD
    GOMBAY, E
    STATISTICS & PROBABILITY LETTERS, 1991, 12 (05) : 421 - 427
  • [4] Asymptotic expansion of the risk of maximum likelihood estimator with respect to -divergence
    Sheena, Yo
    COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2018, 47 (16) : 4059 - 4087
  • [5] Edgeworth expansion for an estimator of the adjustment coefficient
    Brito, Margarida
    Moreira Freitas, Ana Cristina
    INSURANCE MATHEMATICS & ECONOMICS, 2008, 43 (02): : 203 - 208
  • [6] Edgeworth expansion for the kernel quantile estimator
    Maesono, Yoshihiko
    Penev, Spiridon
    ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2011, 63 (03) : 617 - 644
  • [7] An expansion for the maximum likelihood estimator of location and its distribution function
    Venetiaan, Shanti
    BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, 2009, 23 (01) : 82 - 91
  • [8] Edgeworth expansion for the kernel quantile estimator
    Yoshihiko Maesono
    Spiridon Penev
    Annals of the Institute of Statistical Mathematics, 2011, 63 : 617 - 644
  • [9] A nonparametric estimation procedure for the Hawkes process: comparison with maximum likelihood estimation
    Kirchner, M.
    Bercher, A.
    JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 2018, 88 (06) : 1106 - 1116
  • [10] A Regularized Maximum Likelihood Estimator for the Period of a Cyclostationary Process
    Ramirez, David
    Schreier, Peter J.
    Via, Javier
    Santamaria, Ignacio
    Scharf, Louis L.
    CONFERENCE RECORD OF THE 2014 FORTY-EIGHTH ASILOMAR CONFERENCE ON SIGNALS, SYSTEMS & COMPUTERS, 2014, : 1972 - 1976
12345