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arXiv · 0803.0879

Statistical analysis of self-similar conservative fragmentation chains

Marc Hoffmann·Nathalie Krell
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Abstract

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.

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Marc Hoffmann, Nathalie Krell. 2011-02-15. Statistical analysis of self-similar conservative fragmentation chains. https://doi.org/10.3150/10-bej274

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