Electronic Journal of Statistics

Nonparametric estimation for a two-dimensional renewal process

Katherine F. Davies and B. Gail Ivanoff

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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

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

First available in Project Euclid: 31 August 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Point process renewal process avoidance probability multiparameter martingale product limit estimator


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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