Random coefficients bifurcating autoregressive processes
ESAIM: Probability and Statistics, Tome 18 (2014) , pp. 365-399.

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.

DOI : https://doi.org/10.1051/ps/2013042
Classification : 60J05,  60J80,  62M05,  62F12,  60G42,  92D25
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/}
}
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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