Parameters estimation for asymmetric bifurcating autoregressive processes with missing data

被引：13

作者：

de Saporta, Benoite ^{[1
,2
]}

Gegout-Petit, Anne ^{[2
,3
]}

机构：

[1] Univ Bordeaux, GREThA, CNRS, UMR 5113,IMB,UMR 5251, Bordeaux, France

[2] Univ Bordeaux, INRIA Bordeaux Sud Ouest Team CQFD, Bordeaux, France

[3] Univ Bordeaux, IMB, CNRS, UMR 525, Bordeaux, France

来源：

ELECTRONIC JOURNAL OF STATISTICS | 2011年 / 5卷

关键词：

Least squares estimation; bifurcating autoregressive process; missing data; Galton-Watson process; joint model; martingales; limit theorems; MODEL;

D O I：

10.1214/11-EJS643

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：

We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some of the data are missing. In this aim, we model the observed data by a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the strong consistency of our estimators on the set of non-extinction of the Galton-Watson process, via a martingale approach. We also prove a quadratic strong law and the asymptotic normality.

引用

页码：1313 / 1353

页数：41

共 16 条

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[2]

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