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arXiv: 0803.0879

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Bernoulli 17, 1 (2011) 395-423

Statistical analysis of self-similar conservative fragmentation chains

Marc Hoffmann 1, Nathalie Krell 2, 3

(2011)

We explore statistical inference in self-similar conservative fragmentation chains, when only (approximate) observations of the size of the fragments below a given threshold are available. This framework, introduced by Bertoin and Martinez, is motivated by mineral crushing in mining industry. The underlying estimated object is the step distribution of the random walk associated to a randomly tagged fragment that evolves along the genealogical tree representation of the fragmentation process. We compute upper and lower rates of estimation in a parametric framework, and show that in the non-parametric case, the difficulty of the estimation is comparable to ill-posed linear inverse problems of order 1 in signal denoising.

1:	Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA)
	Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8050 – Fédération de Recherche Bézout
2:	Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
	CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot
3:	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne

Subject

:

Mathematics/Statistics Statistics/Statistics Theory Mathematics/Probability

Keyword(s): fragmentation chains – parametric – non-parametric estimation – key renewal theorem

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From: Nathalie Krell <>

Submitted on: Thursday, 6 March 2008 15:27:48

Updated on: Monday, 25 July 2011 17:18:03