Nonparametric estimation for a two-dimensional renewal process

被引：0
|
作者：
Davies, Katherine F. [1 ]
Ivanoff, B. Gail [2 ]
机构：
[1] Univ Manitoba, Dept Stat, Winnipeg, MB R3T 2N2, Canada
[2] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada
来源：
ELECTRONIC JOURNAL OF STATISTICS | 2012年 / 6卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
Point process; renewal process; avoidance probability; multiparameter martingale; product limit estimator;
D O I：
10.1214/12-EJS718
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：
This paper introduces nonparametric estimation methods for spatial point processes satisfying a particular renewal property. Martingale methods yield a unified approach for renewal processes in both one and two dimensions, and can be used for both synchronous and asynchronous data. In each case, we obtain martingale estimators of the avoidance probabilities that characterize the renewal process. Asymptotic properties of the estimators are studied analytically and empirically.
引用
收藏
页码：1449 / 1476
页数：28
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