Random coefficients bifurcating autoregressive processes

Benoîte de Saporta; Anne Gégout-Petit; Laurence Marsalle

ESAIM: Probability and Statistics (2014)

  • Volume: 18, page 365-399
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Saporta, Benoîte de, Gégout-Petit, Anne, and Marsalle, Laurence. "Random coefficients bifurcating autoregressive processes." ESAIM: Probability and Statistics 18 (2014): 365-399. <http://eudml.org/doc/274374>.

@article{Saporta2014,
abstract = {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.},
author = {Saporta, Benoîte de, Gégout-Petit, Anne, Marsalle, Laurence},
journal = {ESAIM: Probability and Statistics},
keywords = {autoregressive process; branching process; missing data; least squares estimation; limit theorems; bifurcating Markov chain; martingale; bifurcating autoregressive process; Galton-Watson tree},
language = {eng},
pages = {365-399},
publisher = {EDP-Sciences},
title = {Random coefficients bifurcating autoregressive processes},
url = {http://eudml.org/doc/274374},
volume = {18},
year = {2014},
}

TY - JOUR
AU - Saporta, Benoîte de
AU - Gégout-Petit, Anne
AU - Marsalle, Laurence
TI - Random coefficients bifurcating autoregressive processes
JO - ESAIM: Probability and Statistics
PY - 2014
PB - EDP-Sciences
VL - 18
SP - 365
EP - 399
AB - 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.
LA - eng
KW - autoregressive process; branching process; missing data; least squares estimation; limit theorems; bifurcating Markov chain; martingale; bifurcating autoregressive process; Galton-Watson tree
UR - http://eudml.org/doc/274374
ER -

References

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