Abstract
Abstract : Blumenthal considered the problem of sequential estimation of the largest of k normal means when a bound is set on the acceptable mean square error. He showed that his procedure results in only a small savings in sample size when compared to a conservative fixed sample procedure for the case of known variance. Carroll criticized this procedure because it does not give the user the flexibility of sampling selectively from the k populations. Carroll defined a procedure which early in the experiment eliminates from further consideration those populations which are obviously not associated with the largest mean and hence provide little relevant information; his theoretical large-sample calculations indicate possible large savings in sample size with no corresponding increase in mean square error. In this paper we contrast the small sample behavior of the two approaches by means of a Monte-Carlo simulation study; both known and unknown variance are considered. (Author)
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