This paper presents a new model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton-Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency, with a convergence rate, and asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new results in both these frameworks.
Mots-clés : autoregressive process, branching process, missing data, least squares estimation, limit theorems, bifurcating Markov chain, martingale
@article{PS_2014__18__365_0,
author = {Saporta, Beno{\^\i}te de and G\'egout-Petit, Anne and Marsalle, Laurence},
title = {Random coefficients bifurcating autoregressive processes},
journal = {ESAIM: Probability and Statistics},
pages = {365--399},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2013042},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2013042/}
}
TY - JOUR AU - Saporta, Benoîte de AU - Gégout-Petit, Anne AU - Marsalle, Laurence TI - Random coefficients bifurcating autoregressive processes JO - ESAIM: Probability and Statistics PY - 2014 SP - 365 EP - 399 VL - 18 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2013042/ DO - 10.1051/ps/2013042 LA - en ID - PS_2014__18__365_0 ER -
%0 Journal Article %A Saporta, Benoîte de %A Gégout-Petit, Anne %A Marsalle, Laurence %T Random coefficients bifurcating autoregressive processes %J ESAIM: Probability and Statistics %D 2014 %P 365-399 %V 18 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2013042/ %R 10.1051/ps/2013042 %G en %F PS_2014__18__365_0
Saporta, Benoîte de; Gégout-Petit, Anne; Marsalle, Laurence. Random coefficients bifurcating autoregressive processes. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 365-399. doi : 10.1051/ps/2013042. http://www.numdam.org/articles/10.1051/ps/2013042/
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