GÉGOUT-PETIT, Anne; DE SAPORTA, Benoîte; MARSALLE, Laurence

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GÉGOUT-PETIT, Anne
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]

DE SAPORTA, Benoîte
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Groupe de Recherche en Economie Théorique et Appliquée [GREThA]

MARSALLE, Laurence
Laboratoire Paul Painlevé - UMR 8524 [LPP]

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International Biometric Society Channel Network 3rd conference, 2011-04-11, Bordeaux.

Résumé en anglais

Bifurcating autoregressive processes (BAR) generalize autoregressive (AR) processes, when the data have a binary tree structure. Typically, they are involved in modelling cell lineage data, since each cell in one generation gives birth to two offspring in the next one. Cell lineage data usually consist of observations of some quantitative characteristic of the cells, over several generations descended from an initial cell. BAR processes take into account both inherited and environmental effects to explain the evolution of the quantitative characteristic under study. They were first introduced by Cowan and Staudte in 1986. We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes when some of the data are missing. We model the process of observed data with a two-type Galton Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the almost sure convergence of our estimators on the set of non-extinction of the Galton Watson process. We also prove a quadratic strong law and a central limit theorem. We give results on real data on growth rate of Escherichia coli (see Stewart & al, Plosbiol 2005).< Réduire

Mots clés en anglais

BIfurcating Autoregressive Processes

Galton-Watson Processes

Almost Sure Convergence

Central Limit Theorem

Martingales.

Martingales

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Bifurcating autoregressive processes with missing data and application to cell division data

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