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Mathematics & Statistics

# Colloquia — Summer 2005

## Friday, May 27, 2005

Title
Speaker

Time
Place

Statistical inference for branching processes
Professor Nikolay Yanev
Department of Probability and Statistics
Institute of Mathematics and Informatics
Sofia, Bulgaria
10:00am-11:00am
PHY 109
George Yanev

Abstract

It is well known that branching processes have a lot of applications, in particular in biology and medicine. We will discuss the asymptotic behavior of branching populations having an increasing random number of ancestors. We will present an estimation theory for the mean, variance, and offspring distributions of the processes $$Z_t(n)$$ with a random number of ancestors $$Z_0(n)$$, as both $$n$$ (and thus $$Z_0(n)$$ in some sense) and $$t\to\infty$$. Non-parametric, consistent, and asymptotically normal estimators will be proposed. Some censored estimators will also be considered. We will show that all results can be transferred to branching processes with immigration, under an appropriate sampling scheme. A software system for simulation and estimation of branching processes will be demonstrated.

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Speaker

Time
Place