Variance Estimators in Branching Processes with Non-Homogeneous Immigration
I. Rahimov, George P. Yanev · Biomath Communications · 2013
Branching processes with immigration were proposed to study the temporal development of populations of differentiated cells in [3] and more recently in [1]. More specifically, terminally differentiated oligodendrocytes of the central nervous system and leukemia cells were analyzed. In both cases the cell population expanded through both division of existing (progenitor) cells and differentiation of stem cells. The population’s viability was preserved by allowing the immigration distribution to vary in time. We construct conditional least-squares estimators for the offspring variance assuming that the immigration mean increases to infinity over time. The asymptotic normality of the proposed estimators is established. Part of the results was published in ...