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Asymptotic Analysis for Bifurcating AutoRegressive Processes via a Martingale Approach


 
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1. Title Title of document Asymptotic Analysis for Bifurcating AutoRegressive Processes via a Martingale Approach
 
2. Creator Author's name, affiliation, country Bernard Bercu; Université de Bordeaux; France
 
2. Creator Author's name, affiliation, country Benoîte de Saporta; Université de Bordeaux; France
 
2. Creator Author's name, affiliation, country Anne Gégout-Petit; Université de Bordeaux; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) bifurcating autoregressive process; tree-indexed times series; martingales; least squares estimation; almost sure convergence; quadratic strong law; central limit theorem
 
3. Subject Subject classification 60F15; 60F05; 60G42
 
4. Description Abstract We study the asymptotic behavior of the least squares estimators of the unknown parameters of general pth-order bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the central limit theorem. All our analysis relies on non-standard asymptotic results for martingales.
 
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7. Date (YYYY-MM-DD) 2009-11-11
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/717
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-717
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
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