The expected cost of an experiment can be reduced through the use of an optimal stopping rule (for deciding whether or not to make further observations) or an optimal sequential allocation rule (for assignment of further subjects to treatments). The difficult analysis of the sampling distribution of the resulting estimators will be attacked using renewal theory and approximations due to asymptotic expansions. These expansions also yield approximations to posterior distributions and are of use in approximating optimal Bayesian designs. Sequential methods of estimation will be applied to the calibration problem as well as nonparametric fixed width confidence intervals.
