Saddlepoint Approximations to the Moments of Multitype Age-Dependent Branching Processes, with Applications
Article first published online: 9 JUN 2009
© 2009, The International Biometric Society
Volume 66, Issue 2, pages 567–577, June 2010
How to Cite
Hyrien, O., Chen, R., Mayer-Pröschel, M. and Noble, M. (2010), Saddlepoint Approximations to the Moments of Multitype Age-Dependent Branching Processes, with Applications. Biometrics, 66: 567–577. doi: 10.1111/j.1541-0420.2009.01281.x
- Issue published online: 1 JUN 2010
- Article first published online: 9 JUN 2009
- Received September 2007. Revised February 2009. Accepted February 2009.
- Cell kinetics;
- Discretely observed stochastic process;
- Saddlepoint approximation
Summary This article proposes saddlepoint approximations to the expectation and variance–covariance function of multitype age-dependent branching processes. The proposed approximations are found accurate, easy to implement, and much faster to compute than by simulating the process. Multiple applications are presented, including the analyses of clonal data on the generation of oligodendrocytes from their immediate progenitor cells, and on the proliferation of Hela cells. New estimators are also constructed to analyze clonal data. The proposed methods are finally used to approximate the distribution of the generation, which has recently found several applications in cell biology.