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Parameters estimation for asymmetric bifurcating autoregressive processes with missing data. (English) Zbl 1274.62192

Summary: 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.

MSC:

62F12 Asymptotic properties of parametric estimators
62M09 Non-Markovian processes: estimation
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60G42 Martingales with discrete parameter
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