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.

引用

页码：365 / 399

页数：35

共 28 条

[1] Proliferating parasites in dividing cells: Kimmel's branching model revisited
Bansaye, Vincent
[J]. ANNALS OF APPLIED PROBABILITY, 2008, 18 (03) : 967 - 996
[2] Non-Gaussian bifurcating models and quasi-li keli hood estimation
Basawa, IV
Zhou, J
[J]. JOURNAL OF APPLIED PROBABILITY, 2004, 41A : 55 - 64
[3] Asymptotic analysis for bifurcating autoregressive processes via a martingale approach
Bercu, Bernard
de Saporta, Benoite
Gegout-Petit, Anne
[J]. ELECTRONIC JOURNAL OF PROBABILITY, 2009, 14 : 2492 - 2526
[4] Blandin V., 2012, ARXIV12042926
[5] THE STOCHASTIC EQUATION YN+1=ANYN+BN WITH STATIONARY COEFFICIENTS
BRANDT, A
[J]. ADVANCES IN APPLIED PROBABILITY, 1986, 18 (01) : 211 - 220
[6] Inference for the random coefficients bifurcating autoregressive model for cell lineage studies
Bui, QM
Huggins, RM
[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1999, 81 (02) : 253 - 262
[7] THE BIFURCATING AUTOREGRESSION MODEL IN CELL LINEAGE STUDIES
COWAN, R
STAUDTE, R
[J]. BIOMETRICS, 1986, 42 (04) : 769 - 783
[8] Tail of the stationary solution of the stochastic equation Yn+1=anYn+bn with Markovian coefficients
de Saporta, B
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2005, 115 (12) : 1954 - 1978
[9] Asymmetry tests for bifurcating auto-regressive processes with missing data
de Saporta, Benoite
Gegout-Petit, Anne
Marsalle, Laurence
[J]. STATISTICS & PROBABILITY LETTERS, 2012, 82 (07) : 1439 - 1444
[10] Parameters estimation for asymmetric bifurcating autoregressive processes with missing data
de Saporta, Benoite
Gegout-Petit, Anne
[J]. ELECTRONIC JOURNAL OF STATISTICS, 2011, 5 : 1313 - 1353

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