Mathematics – Statistics Theory
Scientific paper
2008-03-06
Bernoulli 2011, Vol. 17, No. 1, 395-423
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.3150/10-BEJ274 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti
Scientific paper
10.3150/10-BEJ274
We explore statistical inference in self-similar conservative fragmentation chains when only approximate observations of the sizes of the fragments below a given threshold are available. This framework, introduced by Bertoin and Martinez [Adv. Appl. Probab. 37 (2005) 553--570], is motivated by mineral crushing in the mining industry. The underlying object that can be identified from the data is the step distribution of the random walk associated with 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 nonparametric case, the difficulty of the estimation is comparable to ill-posed linear inverse problems of order 1 in signal denoising.
Hoffmann Marc
Krell Nathalie
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