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First Contact Distribution Function Estimation for a Partially Observed Dynamic Germ-Grain Model with Renewal Dropping Process

In: Math Everywhere

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  • Marcello De Giosa

    (Università di Bari, Dipartimento di Matematica)

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.

Suggested Citation

  • Marcello De Giosa, 2007. "First Contact Distribution Function Estimation for a Partially Observed Dynamic Germ-Grain Model with Renewal Dropping Process," Springer Books, in: Giacomo Aletti & Alessandra Micheletti & Daniela Morale & Martin Burger (ed.), Math Everywhere, pages 51-62, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-44446-6_5
    DOI: 10.1007/978-3-540-44446-6_5
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