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

Marcello De Giosa ()
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Marcello De Giosa: Università di Bari, Dipartimento di Matematica

A chapter in Math Everywhere, 2007, pp 51-62 from Springer

Abstract: 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.

Keywords: Renewal Process; Standard Brownian Motion; Brownian Bridge; Partial Observation; Contact Distribution (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-44446-6_5

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DOI: 10.1007/978-3-540-44446-6_5

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