On the Extinction Probability for Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Branching Processes in Autoregressive Random Environment

2000 Mathematics Subject Classification: 60J80, 60K05.

Subcritical Randomly Indexed Branching Processes

2000 Mathematics Subject Classification: 60J80, 62P05.

Revisiting Offspring Maxima in Branching Processes

2000 Mathematics Subject Classification: 60J80; 60G70.

Using Inside-Outside Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes

Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are particles of different types. Usually such a process is not observable in the sense of the whole tree, but only as the “generation” at a given moment in time, which consists of the number of particles of every type. This requires an EM-type algorithm to obtain a maximum likelihood (ML) estimate of the parameters of the branching process. Using a version of the inside-outside algorithm for stochastic context-free grammars (SCFG), such an estimate could be obtained for the offspring distribution of the process.

Em Estimation of the Offspring Distribution in Mutitype Branching Processes - a Model in Cell Kinetics

2000 Mathematics Subject Classification: 60J80, 60J85, 62P10, 92D25.

Some Contributions to the Class of Two-Sex Branching Processes Depending on the Number of Couples in the Population

2000 Mathematics Subject Classification: 60J80

Robust Estimation in Multitype Branching Processes Based on their Asymptotic Properties

2000 Mathematics Subject Classification: 60J80.

Offspring Mean Estimators in Branching Processes with Immigration

2000 Mathematics Subject Classification: 60J80.

Estimators in Branching Processes with Immigration

2000 Mathematics Subject Classi cation: 60J80.

Statistical Inference for Processes Depending on Environments and Application in Regenerative Processes

We build the Conditional Least Squares Estimator of 0 based on the observation of a single trajectory of {Zk,Ck}k, and give conditions ensuring its strong consistency. The particular case of general linear models according to 0=( 0, 0) and among them, regenerative processes, are studied more particularly. In this frame, we may also prove the consistency of the estimator of 0 although it belongs to an asymptotic negligible part of the model, and the asymptotic law of the estimator may also be calculated.

Parametric Estimation in Branching Processes with an Increasing Random Number of Ancestors

2000 Mathematics Subject Classification: 60J80, 62M05

Extremes of Bivariate Geometric Variables with Application to Bisexual Branching Processes

2000 Mathematics Subject Classification: 60J80, 60G70.

Simulation and Robust Modifications of Estimates in Branching Processes

This study is focused on the comparison and modification of different estimates arising in the branching processes. Simulations of models with or without migration are put through. Due to the complexity of the computations the algorithms are designed with the language of technical computing MATLAB. Using the simulations, estimates of the o spring mean of the generated processes are calculated. It is well known in the literature that under certain conditions the asymptotic distribution of the estimates is proved to be normal. Using the asymptotic normality a modified method of maximum likelihood is proposed. The aim is to obtain trimmed maximum likelihood estimates based on several sample paths with the same number of generations. Thus in a natural way the observations, inconsistent with the aprior information about the asymptotic normality are excluded from the model. The computation of the standard error allows the comparison of different types of estimates.