B1572
Title: Bahadur-type asymptotics for estimates of ancestor mean of branching processes with immigration
Authors: Anand Vidyashankar - George Mason University (United States) [presenting]
Abstract: Let $\{Z_{n, j}: n \ge 1, j \ge 1\}$ denote a collection of, possibly correlated, identically distributed branching processes initiated by $\{Z_{0, j}: j \ge 1\}$ ancestors. Let $\{I_{n,j}: n \ge 1, j \ge 1\}$ denote the corresponding sequences of immigration random variables. When the collection of branching processes are i.i.d. (no immigration) and supercritical, it was shown in a prior study that $\hat{m}_A= [\sum_{j=1}^{r(n)} Z_{n, j}][\hat{m}_o^n]^{-1}$ is a consistent and asymptotically normal estimator of $m_A$. This theory is extended to a very general collection of branching processes, possibly with immigration, and establishes sharp concentration inequalities for the ancestor mean estimator. A key technical tool involves Bahadur-type asymptotics for the estimator of the ancestral mean.
