| Issue |
ESAIM: PS
Volume 18, 2014
|
|
|---|---|---|
| Page(s) | 365 - 399 | |
| DOI | https://doi.org/10.1051/ps/2013042 | |
| Published online | 03 October 2014 | |
Random coefficients bifurcating autoregressive processes
1 Univ. Bordeaux, Gretha, UMR 5113,
IMB, UMR 5251, 33400 Talence, France CNRS, Gretha, UMR 5113, IMB, UMR
5251, 33400 Talence, France INRIA
Bordeaux Sud Ouest, team CQFD, 33400
Talence,
France
2 Univ. Bordeaux, IMB, UMR 5251, 33400
Talence, France CNRS, IMB, UMR 5251, 33400 Talence, France INRIA Bordeaux Sud Ouest, team
CQFD, 33400
Talence,
France
3 Univ. Lille 1, Laboratoire Paul
Painlevé, UMR 8524, 59655 Villeneuve d’Ascq, France CNRS, Laboratoire Paul Painlevé,
UMR 8524, 59655
Villeneuve d’Ascq,
France
benoite.desaporta@math.u-bordeaux1.fr
Received:
19
October
2012
Revised:
3
May
2013
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.
Mathematics Subject Classification: 60J05 / 60J80 / 62M05 / 62F12 / 60G42 / 92D25
Key words: Autoregressive process / branching process / missing data / least squares estimation / limit theorems / bifurcating Markov chain / martingale
© EDP Sciences, SMAI 2014
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