Electronic Journal of Statistics

Nonparametric estimation for a two-dimensional renewal process

Katherine F. Davies and B. Gail Ivanoff

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 1449-1476.

Dates
First available in Project Euclid: 31 August 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1346421600

Digital Object Identifier
doi:10.1214/12-EJS718

Mathematical Reviews number (MathSciNet)
MR2988454

Zentralblatt MATH identifier
1337.62300

Subjects
Primary: 60K05: Renewal theory 62G05: Estimation
Secondary: 62M30: Spatial processes 60G55: Point processes

Keywords
Point process renewal process avoidance probability multiparameter martingale product limit estimator

Citation

Davies, Katherine F.; Ivanoff, B. Gail. Nonparametric estimation for a two-dimensional renewal process. Electron. J. Statist. 6 (2012), 1449--1476. doi:10.1214/12-EJS718. https://projecteuclid.org/euclid.ejs/1346421600


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