Estimation of the intensity of non-homogeneous point processes via wavelets

被引：6
|
作者：
Simon de Miranda, Jose Carlos [1 ]
Morettin, Pedro A. [1 ]
机构：
[1] Inst Math & Stat, Dept Stat, BR-05311970 Sao Paulo, Brazil
来源：
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 2011年 / 63卷 / 06期
基金：
巴西圣保罗研究基金会;
关键词：
Intensity; Non-internally correlated point processes; Point processes; Poisson processes; Threshold; Wavelets; SHRINKAGE;
D O I：
10.1007/s10463-010-0283-8
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：
In this article we consider the problem of estimating the intensity of a non-homogeneous point process on the real line. The approach used is via wavelet expansions. Estimators of the intensity are proposed and their properties are studied, including the case of thresholded versions. Properties of the estimators for non-homogeneous Poisson processes follow as special cases. An application is given for the series of daily Dow Jones indices. Extensions to more general settings are also indicated.
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页码：1221 / 1246
页数：26
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