Electronic Journal of Statistics

Parameters estimation for asymmetric bifurcating autoregressive processes with missing data

Benoîte de Saporta, Anne Gégout-Petit, and Laurence Marsalle

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 5 (2011), 1313-1353.

Dates
First available in Project Euclid: 19 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1319028570

Digital Object Identifier
doi:10.1214/11-EJS643

Mathematical Reviews number (MathSciNet)
MR2842907

Zentralblatt MATH identifier
1274.62192

Subjects
Primary: 62F12: Asymptotic properties of estimators 62M09: Non-Markovian processes: estimation
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 92D25: Population dynamics (general) 60G42: Martingales with discrete parameter

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

Citation

de Saporta, Benoîte; Gégout-Petit, Anne; Marsalle, Laurence. Parameters estimation for asymmetric bifurcating autoregressive processes with missing data. Electron. J. Statist. 5 (2011), 1313--1353. doi:10.1214/11-EJS643. https://projecteuclid.org/euclid.ejs/1319028570


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