ON SOME RESULTS CONCERNING STOPPING RULES.
JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF STATISTICS
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As a part of the investigation of sequential fixed-width confidence interval procedures for estimating the common mean of two distributions having unequal variances, it was found necessary to extend some of the results of Chow and Robbins Ann. Math. Statist. 36 1965 457-462 to cover somewhat more general kinds of stopping rules. For example, although Chow and Robbins treat only one-sided stopping boundaries, the present investigation requires one to consider two-sided or even many-sided stopping boundaries. Further, some of the boundaries of interest have a slightly more general functional form than do the stopping boundaries discussed in the Chow-Robbins paper. The results given in the present paper provide first-order asymptotic results for the distribution and expected value of the various stopping variables N the random number of observations taken considered, the form of the results being similar to those announced in the Chow-Robbins paper referred to above. Author
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