  We provide deviation inequalities for properly normalized sums of bifurcating
Markov chains on Galton-Watson tree. These processes are extension of
bifurcating Markov chains (which was introduced by Guyon to detect cellular
aging from cell lineage) in case the index set is a binary Galton-Watson
process. As application, we derive deviation inequalities for the least-squares
estimator of autoregressive parameters of bifurcating autoregressive processes
with missing data. These processes allow, in case of cell division, to take
into account the cell's death. The results are obtained under an uniform
geometric ergodicity assumption of an embedded Markov chain.
