Conventional bootstrap and normal confidence interval estimation under adaptive cluster sampling

We examine the performances of bootstrap and normal confidence interval methods for estimating the parametric total when using the Horvitz - Thompson type estimator under adaptive cluster sampling via simulation. On the basis of this and previous work, we include recommendations on using confidence interval methods under adaptive cluster sampling. Two Poisson spatially clustered populations and three sample sizes were used in our simulations. The bootstrap methods ( Gross, McCarthy and Snowden, and Sitter) were based on resampling the original sample of units. All four interval estimation methods performed poorly. On average, bootstrap confidence interval estimates underestimated the parametric totals, resulting in empirical coverages lower than the set confidence level. Coverages for the normal method depended on initial sample sizes and population. In general, if confidence interval estimates are required under adaptive cluster sampling, we recommend using bootstrap interval estimation with the Hansen - Hurwitz type estimator instead of interval estimation with the Horvitz - Thompson type estimator.