• Bernoulli
  • Volume 17, Number 1 (2011), 395-423.

Statistical analysis of self-similar conservative fragmentation chains

Marc Hoffmann and Nathalie Krell

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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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Bernoulli, Volume 17, Number 1 (2011), 395-423.

First available in Project Euclid: 8 February 2011

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fragmentation chains key renewal theorem nonparametric estimation parametric


Hoffmann, Marc; Krell, Nathalie. Statistical analysis of self-similar conservative fragmentation chains. Bernoulli 17 (2011), no. 1, 395--423. doi:10.3150/10-BEJ274.

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