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

页码：277 / 325

页数：49

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