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Semi-parametric inference for the absorption features of a growth-fragmentation model

Azaïs, Romain; Genadot, Alexandre (2014), Semi-parametric inference for the absorption features of a growth-fragmentation model, TEST, 24, 2, p. 341-360. http://dx.doi.org/10.1007/s11749-014-0410-6

Type
Article accepté pour publication ou publié
Date
2014
Journal name
TEST
Volume
24
Number
2
Publisher
Springer
Pages
341-360
Publication identifier
Metadata
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Author(s)
Azaïs, Romain

Genadot, Alexandre
Abstract (EN)
In the present paper, we focus on semi-parametric methods for estimating the absorption probability and the distribution of the absorbing time of a growth-fragmentation model observed within a long time interval. We establish that the absorption probability is the unique solution in an appropriate space of a Fredholm equation of the second kind whose parameters are unknown. We estimate this important characteristic of the underlying process by solving numerically the estimated Fredholm equation. Even if the study has been conducted for a particular model, our method is quite general.
Subjects / Keywords
Non-ergodic piecewise-deterministic Markov process; Growth-fragmentation process; Semi-parametric estimation; Absorption probability; Fredholm integral equation