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

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  • Romain Azaïs
  • Alexandre Genadot

Abstract

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. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • Romain Azaïs & Alexandre Genadot, 2015. "Semi-parametric inference for the absorption features of a growth-fragmentation model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 341-360, June.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:2:p:341-360
    DOI: 10.1007/s11749-014-0410-6
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    References listed on IDEAS

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    4. Chiquet, Julien & Limnios, Nikolaos, 2008. "A method to compute the transition function of a piecewise deterministic Markov process with application to reliability," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1397-1403, September.
    5. Raimund M. Kovacevic & Georg Ch. Pflug, 2011. "Does Insurance Help to Escape the Poverty Trap?—A Ruin Theoretic Approach," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(4), pages 1003-1028, December.
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    Cited by:

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    2. Jos'e Miguel Flores-Contr'o & S'everine Arnold, 2023. "The Role of Direct Capital Cash Transfers Towards Poverty and Extreme Poverty Alleviation -- An Omega Risk Process," Papers 2401.06141, arXiv.org, revised Feb 2024.

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