One-sided coverage intervals for a proportion estimated from a stratified simple random sample
Using an Edgeworth expansion to speed up the asymptotics, we develop one-sided coverage intervals for a proportion based on a stratified simple random sample. To this end, we assume the values of the population units are generated from independent random variables with a common mean within each stratum. These stratum means, in turn, may either be free to vary or are assumed to be equal. The more general assumption is equivalent to a model-free randomization-based framework when finite population correction is ignored. Unlike when an Edgeworth expansion is used to construct one-sided intervals under simple random sampling, it is necessary to estimate the variance of the estimator for the population proportion when the stratum means are allowed to differ. As a result, there may be accuracy gains from replacing the normal z-score in the Edgeworth expansion with a t-score.
Kott, P., & Liu, YK. (2009). One-sided coverage intervals for a proportion estimated from a stratified simple random sample. International Statistical Review, 77(2), 251-265. https://doi.org/10.1111/j.1751-5823.2009.00081.x