Abstract
We consider a partially observed dynamic germ-grain model Θ = {Θ(t) : t ≥ 0} whose grains drop on the plane ℝ2 at times of a renewal process. The first contact distribution at time t is the distribution function of the distance from a fixed point 0 to the nearest point of Θ(t), where the distance is measured using scalar dilations of a fixed test set B. Due to partial observation of the model, an estimation problem arises for the first contact distribution function. We propose a product integral type estimator. Its asymptotic properties are studied.
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Giosa, M.D. (2007). First Contact Distribution Function Estimation for a Partially Observed Dynamic Germ-Grain Model with Renewal Dropping Process. In: Aletti, G., Micheletti, A., Morale, D., Burger, M. (eds) Math Everywhere. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44446-6_5
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DOI: https://doi.org/10.1007/978-3-540-44446-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44445-9
Online ISBN: 978-3-540-44446-6
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