Bifurcating time series models for cell lineage data

This dissertation studies bifurcating time series models. Our motivation comes from cell lineage data, in which each individual in a generation gives rise to two individuals in the next generation. For general bifurcating autoregressive models, asymptotic normality of least squares estimators of model parameters is established. An application to integervalued autoregression is given. For the first-order bifurcating autoregressive process with exponential innovations, exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter are derived. Limit distributions for stationary, critical and explosive cases are unified via a single pivot using a random normalization. The pivot is shown to be asymptotically exponential for all values of the autoregressive parameter. Finally, a general class of Markovian non-Gaussian bifurcating models is studied. Examples include bifurcating autoregression, random coefficient autoregression, bivariate exponential, bivariate gamma, and bivariate Poisson models. Quasilikelihood estimation for the model parameters and large-sample properties of the estimates are discussed.