On empirical Bayes with sequential component

Laippala (1979, Scand. J. Statist., 6, 113–118, correction note, 7, 105; 1985, Ann. Inst. Statist. Math., 37, 315–327) has defined a concept within the empirical Bayes framework that he calls floating optimal sample size. We examine this concept and show that it is one of many possibilities resulting from restricting the class of component sampling procedures in the empirical Bayes decision problem with a sequential component. All ideas are illustrated with the finite state component.