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Improving the fully sequential sampling scheme of Anscombe-Chow-Robbins. (English) Zbl 0942.62091
Summary: A new sequential sampling scheme is proposed in which, after an initial batch sample, sampling is continued in batches of data-dependent sizes (at most $$k$$ such batches), and then one-at-a-time with a data-dependent stopping rule. This new scheme requires about the same sample size as the fully sequential Anscombe-Chow-Robbins (ACR) sampling scheme [F. J. Anscombe, J. R. Stat. Soc. Ser. B 15, 1-29 (1953; Zbl 0050.36301); H. Robbins, Probability and Statistics, H. Cramér Vol., 235-245 (1959; Zbl 0095.13005); Y. S. Chow and H. Robbins, Ann. Math. Stat. 36, 457-462 (1965; Zbl 0142.15601)] but substantially fewer sampling operations. The problem of constructing fixed-width confidence intervals for the mean of a normal population with unknown variance is used as an illustration.

##### MSC:
 62L12 Sequential estimation 62F25 Parametric tolerance and confidence regions 62E99 Statistical distribution theory
##### Keywords:
stopping time; sequential sampling; confidence intervals
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