On the empirical Bayes approach to multiple decision problems with sequential components

The empirical Bayes approach to multiple decision problems with a sequential decision problem as the component is studied. An empirical Bayesm-truncated sequential decision procedure is exhibited for general multiple decision problems. With a sequential component, an empirical Bayes sequential decision procedure selects both a stopping rule function and a terminal decision rule function for use in the component. Asymptotic results are presented for the convergence of the Bayes risk of the empirical Bayes sequential decision procedure.