Identification of multitype branching processes

We solve the problem of constructing an asymptotic global confidence region for the means and the covariance matrices of the reproduction distributions involved in a supercritical multitype branching process. Our approach is based on a central limit theorem associated with a quadratic law of large numbers performed by the maximum likelihood or the multidimensional Lotka-Nagaev estimator of the reproduction law means. The extension of this approach to the least squares estimator of the mean matrix is also briefly discussed. On resout le probleme de construction d'une region de confiance asymptotique et globale pour les moyennes et les matrices de covariance des lois de reproduction d'un processus de branchement multitype et supercritique. Notre approche est basee sur un theoreme de limite centrale associe a une loi forte quadratique verifiee par l'estimateur du maximum de vraisemblance ou l'estimateur multidimensionnel de Lotka-Nagaev des moyennes des lois de reproduction. L'extension de cette approche a l'estimateur des moindres carres de la matrice des moyennes est aussi brievement commentee.

• Publication year

  2000

• Venue

  Annals of Statistics

• Publication date

  2000-12-01

• Fields of study

  Not labeled

• Identifiers
  DOI 10.1214/009053605000000561arXiv math/0603071
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• INVARIANCE PRINCIPLES WITH LOGARITHMIC AVERAGING FOR MARTINGALES

  2001cited by this paper
• Théorèmes limites avec poids pour les martingales vectorielles

  2000cited by this paper
• Généralisation du théorème de la limite centrale presque-sûr pour les martingales vectorielles

  1998cited by this paper
• A joint estimator for the eigenvalues of the reproduction mean matrix of a multitype Galton-Watson process

  1997influential reference
• Vitesse de convergence en loi de l'estimateur des moindres carrés d'un modèle autorégressif (cas mixte)

  1996cited by this paper
• Random iterative models

  1996cited by this paper
• Version forte du théorème de la limite centrale fonctionnel pour les martingales

  1996cited by this paper
• Two Theorems on Convergence in Distribution for Stochastic Integrals and Statistical Applications

  1994influential reference
• Statistical Inference for Branching Processes

  1992cited by this paper
• On the Limit Distributions of Some Functionals in Multi-Type Branching Processes

  1991cited by this paper
• Multitype Branching Processes

  1985cited by this paper
• Asymptotic Properties of Least-Squares Estimates in Stochastic Regression Models

  1985cited by this paper
• Estimation of the variance for the multitype Galton–Watson process

  1982influential reference
• Recurrence formula and the maximum likelihood estimation of the age in a simple branching process

  1982influential reference
• Martingale Limit Theory and Its Application

  1980cited by this paper
• Martingale central limit theorems and asymptotic estimation theory for multitype branching processes

  1978influential reference
• Estimation of the Variance of a Branching Process

  1975cited by this paper
• On estimating the variance of the offspring distribution in a simple branching process

  1974influential reference
• Estimation of the mean and the initial probabilities of a branching process

  1974cited by this paper
• Multitype Branching Processes.

  1973influential reference
• Improved classical limit analogues for Galton-Watson processes with or without immigration

  1971cited by this paper
• Analogues of Classical Limit Theorems for the Supercritical Galton-Watson Process with Immigration

  1971cited by this paper
• Additional Limit Theorems for Indecomposable Multidimensional Galton-Watson Processes

  1966cited by this paper
• A Limit Theorem for Multidimensional Galton-Watson Processes

  1966cited by this paper

• Limit models for a new general class of multitype branching processes with memory and population dependence

  2023cites this paper
• Maximum likelihood estimation for spinal-structured trees

  2021cites this paper
• Self-normalized Cramér moderate deviations for a supercritical Galton–Watson process

  2021cites this paper
• Galton-Watson Process and Bayesian Inference: A Turnkey Method for the Viability Study of Small Populations

  2019cites this paper
• Understanding Cascading Failures

  2018cites this paper
• Multilevel Monte Carlo methods and statistical inference for financial models

  2017influential citation
• Estimating the Propagation of Interdependent Cascading Outages With Multi-Type Branching Processes

  2014cites this paper
• Estimating the Propagation of Several Cascading Outages with Multi-type Branching Processes

  2014cites this paper
• Contribution à l'estimation et au contrôle de processus stochastiques

  2013cites this paper
• Contribution à la statistique des processus : modélisation et applications

  2012cites this paper
• Statistical study of asymmetry in cell lineage data

  2012cites this paper
• Limit models for a new general class of multitype branching processes with memory and population dependence

  2011cites this paper
• Parameters estimation for asymmetric bifurcating autoregressive processes with missing data

  2010cites this paper
• Conditional least squares estimation in nonstationary nonlinear stochastic regression models

  2010cites this paper
• Sur l'identification d'un processus de branchement surcritique

  2009influential citation
• Inference for Partially Observed Multitype Branching Processes and Ecological Applications

  2009influential citation
• LIMIT THEOREMS FOR BIFURCATING MARKOV CHAINS. APPLICATION TO THE DETECTION OF CELLULAR AGING BY JULIEN GUYON

  2008cites this paper
• A MOMENT APPROACH FOR THE ALMOST SURE CENTRAL LIMIT THEOREM FOR MARTINGALES

  2008cites this paper
• Detection of cellular aging in a Galton-Watson process

  2008cites this paper
• Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging

  2007cites this paper
• On Carleman approach for the almost sure central limit theorem for martingales

  2005cites this paper
• Estimation of the offspring mean in a supercritical or near-critical size-dependent branching process

  2004cites this paper
• about the Internet and Networking : 2010 – 2019

  2003cites this paper
• Théorèmes limites avec poids pour les martingales vectorielles

  2000cites this paper