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Journal Articles Electronic Journal of Statistics Year : 2011

Parameters estimation for asymmetric bifurcating autoregressive processes with missing data

Abstract

We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some of the data are missing. In this aim, we model the observed data by 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 strong consistency of our estimators on the set of non-extinction of the Galton-Watson process, via a martingale approach. We also prove a quadratic strong law and the asymptotic normality.

Dates and versions

hal-00545447 , version 1 (10-12-2010)

Identifiers

Cite

Benoîte de Saporta, Anne Gégout-Petit, Laurence Marsalle. Parameters estimation for asymmetric bifurcating autoregressive processes with missing data. Electronic Journal of Statistics , 2011, 5, pp.1313-1353. ⟨10.1214/11-EJS643⟩. ⟨hal-00545447⟩
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