Bootstrap Confidence Intervals for the Population Mean Under Inverse Sampling Design

Inverse sampling is commonly used for surveying rare (but not clustered) populations. However, when the sample size from the rare group is chosen too small, the customary unbiased estimator of the population mean appears to be highly skewed. In such a case, confidence intervals based on asymptotic normal theory have coverage rate smaller than the nominal level. As an approach to overcome this problem, we propose two resampling methods consisting of with-replacement bootstrap (BWR) and without replacement bootstrap (BWO) to construct confidence intervals for the population mean under simple inverse sampling without replacement. We carried out a simulation study to evaluate the behavior of suggested bootstrap methods, the normal approximation and the logarithmic transformation methods. Our simulation results suggest that the BWO method is preferable, since it provides intervals with coverage rate closer to the nominal level together with more balanced error rate.