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

[21] Hugins RM, 2000, AUST NZ J STAT, V42, P423
[22] Asymptotic optimal inference for multivariate branching-Markov processes via martingale estimating functions and mixed normality
Hwang, S. Y.
Basawa, I. V.
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2011, 102 (06) : 1018 - 1031
[23] Branching Markov processes and related asymptotics
Hwang, S. Y.
Basawa, I. V.
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2009, 100 (06) : 1155 - 1167
[24] Nicholls D.F., 1982, LECT NOTES STAT, V11
[25] Aging and death in an organism that reproduces by morphologically symmetric division
Stewart, EJ
Madden, R
Paul, G
Taddei, F
[J]. PLOS BIOLOGY, 2005, 3 (02) : 295 - 300
[26] ADAPTIVE PREDICTION BY LEAST-SQUARES PREDICTORS IN STOCHASTIC REGRESSION-MODELS WITH APPLICATIONS TO TIME-SERIES
WEI, CZ
[J]. ANNALS OF STATISTICS, 1987, 15 (04) : 1667 - 1682
[27] Maximum likelihood estimation for a first-order bifurcating autoregressive process with exponential errors
Zhou, J
Basawa, IV
[J]. JOURNAL OF TIME SERIES ANALYSIS, 2005, 26 (06) : 825 - 842
[28] Least-squares estimation for bifurcating autoregressive processes
Zhou, J
Basawa, IV
[J]. STATISTICS & PROBABILITY LETTERS, 2005, 74 (01) : 77 - 88

← 1 2 3 →