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, via a martingale approach. We also
prove a quadratic strong law and the asymptotic normality