Parameters estimation for asymmetric bifurcating autoregressive processes with missing data

Parameters estimation for asymmetric bifurcating autoregressive processes with missing data

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 le...

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Veröffentlicht in:Electronic journal of statistics 2011-01, Vol.5 (none), p.1313-1353
Hauptverfasser: de Saporta, Benoîte, Gégout-Petit, Anne, Marsalle, Laurence
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Statistics Theory
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creator de Saporta, Benoîte
Gégout-Petit, Anne
Marsalle, Laurence
description 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.
doi_str_mv 10.1214/11-EJS643
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subjects Mathematics
Probability
Statistics
Statistics Theory
title Parameters estimation for asymmetric bifurcating autoregressive processes with missing data
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