Winnicki will study estimation problems for the branching process with immigration. This research builds on his unified theory, which allows inference regardless of the range of parameters. Open questions to be resolved involve asymptotic properties. Tools to be used include functional convergence and stochastic calculus. General optimality questions will be studied using methods of estimating equations and quasi- likelihood. Extensions to non-homogeneous nearly-critical and multitype branching processes will be considered. This research will contribute to the developing field of statistical inference for stochastic processes.
