Asymptotically Optimal Sequential Estimation of the Mean Based on Inclusion Principle
This work addresses statistical inference for mean values in sciences and engineering, but appears incremental as it builds on existing sequential methods.
The paper tackles the problem of constructing random intervals with specified coverage probabilities for the mean using sequential data, showing that this can be achieved by comparing interval endpoints with confidence sequences and deriving asymptotic results.
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference of mean values based on accumulated observational data. We show that the construction of such random intervals can be accomplished by comparing the endpoints of random intervals with confidence sequences for the mean. Asymptotic results are obtained for such sequential methods.