Asymmetry tests for Bifurcating Auto-Regressive Processes with missing data

Benoîte de Saporta (1, 2, 3) , Anne Gégout-Petit (1, 2) , Laurence Marsalle (4)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability
3 GREThA - Groupe de Recherche en Economie Théorique et Appliquée
4 LPP - Laboratoire Paul Painlevé - UMR 8524

We present symmetry tests for bifurcating autoregressive processes (BAR) when some data are missing. BAR processes typically model cell division data. Each cell can be of one of two types \emph{odd} or \emph{even}. The goal of this paper is to study the possible asymmetry between odd and even cells in a single observed lineage. We first derive asymmetry tests for the lineage itself, modeled by a two-type Galton-Watson process, and then derive tests for the observed BAR process. We present applications on both simulated and real data.

Domaines: Théorie [stat.TH]

Benoîte de Saporta, Anne Gégout-Petit, Laurence Marsalle. Asymmetry tests for Bifurcating Auto-Regressive Processes with missing data. Statistics and Probability Letters, 2012, 82 (7), pp.1439-1444. ⟨10.1016/j.spl.2012.04.003⟩. ⟨hal-00662129⟩