We show that if an appropriate stopping rule is used to determine the sample size when estimating the parameters in a stationary and ergodic threshold AR(1) model, then the sequential least-squares estimator is asymptotically risk efficient. The stopping rule is also shown to be asymptotically...

For the problem of estimating the offspring mean of a branching process with immigration, we propose a modification of the sequential estimator of considered in Sriram et al. (, Ann. Statist.) and study its nonasymptotic and asymptotic properties. In the nonasymptotic setting, it is shown that...

In this paper we consider bootstrap approximation to the sampling distribution of an estimator of the offspring mean m in a branching process with immigration. A modification of the standard parametric bootstrap procedure is shown to eliminate the invalidity of the standard bootstrap for the...