Open Access
2012 Nonparametric estimation for a two-dimensional renewal process
Katherine F. Davies, B. Gail Ivanoff
Electron. J. Statist. 6: 1449-1476 (2012). DOI: 10.1214/12-EJS718


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.


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Katherine F. Davies. B. Gail Ivanoff. "Nonparametric estimation for a two-dimensional renewal process." Electron. J. Statist. 6 1449 - 1476, 2012.


Published: 2012
First available in Project Euclid: 31 August 2012

zbMATH: 1337.62300
MathSciNet: MR2988454
Digital Object Identifier: 10.1214/12-EJS718

Primary: 60K05 , 62G05
Secondary: 60G55 , 62M30

Keywords: avoidance probability , multiparameter martingale , point process , product limit estimator , Renewal process

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

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