RANDOM COEFFICIENTS BIFURCATING AUTOREGRESSIVE PROCESSES

被引：7
|
作者：
de Saporta, Benoite [1 ,2 ,3 ]
Gegout-Petit, Anne [4 ,5 ,6 ]
Marsalle, Laurence [7 ,8 ]
机构：
[1] Univ Bordeaux, Gretha, UMR 5113, IMB,UMR 5251, F-33400 Talence, France
[2] CNRS, Gretha, UMR 5113, IMB,UMR 5251, F-33400 Talence, France
[3] INRIA Bordeaux Sud Ouest, Team CQFD, F-33400 Talence, France
[4] Univ Bordeaux, IMB, UMR 5251, F-33400 Talence, France
[5] CNRS, IMB, UMR 5251, F-33400 Talence, France
[6] INRIA Bordeaux Sud Ouest, Team CQFD, F-33400 Talence, France
[7] Univ Lille 1, Lab Paul Painleve, UMR 8524, F-59655 Villeneuve Dascq, France
[8] CNRS, Lab Paul Painleve, UMR 8524, F-59655 Villeneuve Dascq, France
来源：
ESAIM-PROBABILITY AND STATISTICS | 2014年 / 18卷
关键词：
Autoregressive process; branching process; missing data; least squares estimation; limit theorems; bifurcating Markov chain; martingale; VARIANCE-COMPONENTS MODELS; INFERENCE;
D O I：
10.1051/ps/2013042
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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.
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页码：365 / 399
页数：35
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