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

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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 : 10.1051/ps/2013042
Classification : 60J05, 60J80, 62M05, 62F12, 60G42, 92D25
Keywords: 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://geodesic.mathdoc.fr/articles/10.1051/ps/2013042/}
}
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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

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