Information inequalities for the minimax risk of sequential estimators are derived in the case where the loss is measured by the squared error of estimation plus a linear functional of the number of observations. The results are applied to construct minimax sequential estimators of: the failure rate in an exponential model with censored data, the expected proportion of uncensored observations in the proportional hazards model, the odds ratio in a binomial distribution and the expectation of exponential...

Inverse sampling and formal sequential designs may prove useful in reducing the sample size in studies where a small population proportion p is compared with a hypothesized reference proportion p0. These methods are applied to the design of a cytogenetic study about chromosomal abnormalities in men with a daughter affected by Turner's syndrome. First it is shown how the calculated sample size for a classical design depends on the parameterization used. Later this sample size is compared with the...