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Relative frequencies in multitype branching processes

by: Andrei Y. Yakovlev, and Nikolay M. Yanev

(2009) .

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URL:	http://arxiv.org/abs/0902.4773

This paper considers the relative frequencies of distinct types of individuals in multitype branching processes. We prove that the frequencies are asymptotically multivariate normal when the initial number of ancestors is large and the time of observation is fixed. The result is valid for any branching process with a finite number of types; the only assumption required is that of independent individual evolutions. The problem under consideration is motivated by applications in the area of cell biology. Specifically, the reported limiting results are of advantage in cell kinetics studies where the relative frequencies but not the absolute cell counts are accessible to measurement. Relevant statistical applications are discussed in the context of asymptotic maximum likelihood inference for multitype branching processes.

Description

[0902.4773] Relative frequencies in multitype branching processes

BibTeX record

@misc{Yakovlev2009,
  abstract = {  This paper considers the relative frequencies of distinct types of
individuals in multitype branching processes. We prove that the frequencies are
asymptotically multivariate normal when the initial number of ancestors is
large and the time of observation is fixed. The result is valid for any
branching process with a finite number of types; the only assumption required
is that of independent individual evolutions. The problem under consideration
is motivated by applications in the area of cell biology. Specifically, the
reported limiting results are of advantage in cell kinetics studies where the
relative frequencies but not the absolute cell counts are accessible to
measurement. Relevant statistical applications are discussed in the context of
asymptotic maximum likelihood inference for multitype branching processes.
},
  added-at = {2009-07-09T00:05:35.000+0200},
  author = {Yakovlev, Andrei Y. and Yanev, Nikolay M.},
  biburl = {http://www.bibsonomy.org/bibtex/22e1ed1de4ab36e19ccea06c8634111d6/ebo},
  description = {[0902.4773] Relative frequencies in multitype branching processes},
  interhash = {b2e1afdc21649b00811aaf27cb265790},
  intrahash = {2e1ed1de4ab36e19ccea06c8634111d6},
  keywords = {branching imported stochastic},
  note = {cite arxiv:0902.4773
Comment: Published in at http://dx.doi.org/10.1214/08-AAP539 the Annals of
  Applied Probability (http://www.imstat.org/aap/) by the Institute of
  Mathematical Statistics (http://www.imstat.org)},
  timestamp = {2009-07-09T00:05:35.000+0200},
  title = {Relative frequencies in multitype branching processes},
  url = {http://arxiv.org/abs/0902.4773},
  year = 2009
}

Endnote record

%0 Generic
%1 Yakovlev2009
%A Yakovlev, Andrei Y.
%A Yanev, Nikolay M.
%D 2009
%K 
%T Relative frequencies in multitype branching processes
%U http://arxiv.org/abs/0902.4773
%X   This paper considers the relative frequencies of distinct types of
individuals in multitype branching processes. We prove that the frequencies are
asymptotically multivariate normal when the initial number of ancestors is
large and the time of observation is fixed. The result is valid for any
branching process with a finite number of types; the only assumption required
is that of independent individual evolutions. The problem under consideration
is motivated by applications in the area of cell biology. Specifically, the
reported limiting results are of advantage in cell kinetics studies where the
relative frequencies but not the absolute cell counts are accessible to
measurement. Relevant statistical applications are discussed in the context of
asymptotic maximum likelihood inference for multitype branching processes.