Validity of sequential bootstrap for subcritical and critical branching processes

Abstract

Sequential bootstrapping for branching processes with immigration is proposed. The asymptotic validity of a sequential bootstrap estimator of the offspring mean in is estabilished for all values of m ∊ (0, 1]. This result is to be constrasted with the standard (non-sequential)bootstrapping where the bootstrap estimator estimator has been shown to asymptotically invalid (see, Sriram (1992)).

Keywords:

• Sub-critical and critical branching processes
• sequential bootstrap