Abstract
For the product of two population means, the problem of constructing a fixed-width confidence interval with preassigned coverage probability is considered. It is shown that the optimal sample sizes which minimize the total sample size and at the same time guarantee a fixed-width confidence interval of desired coverage depend on the unknown parameters. In order to overcome this, a fully sequential procedure consisting of a sampling scheme and a stopping rule are proposed. It is then shown that the sequential confidence interval is asymptotically consistent and the stopping rule is asymptotically efficient, as the width goes to zero. Furthermore, a second order result for the difference between the expected stopping time and the (total) optimal fixed sample size is established. The theoretical results are supported by appropriate simulations.
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Zheng, S., Sriram, T.N. & Seila, A.F. Sequential Fixed-Width Confidence Interval for the Product of Two Means. Annals of the Institute of Statistical Mathematics 50, 119–145 (1998). https://doi.org/10.1023/A:1003453431570
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DOI: https://doi.org/10.1023/A:1003453431570