A Comparison of Existing Bootstrap Algorithms for Multi-Stage Sampling Designs

Multi-stage sampling designs are often used in household surveys because a sampling frame of elements may not be available or for cost considerations when data collection involves face-to-face interviews. In this context, variance estimation is a complex task as it relies on the availability of second-order inclusion probabilities at each stage. To cope with this issue, several bootstrap algorithms have been proposed in the literature in the context of a two-stage sampling design. In this paper, we describe some of these algorithms and compare them empirically in terms of bias, stability, and coverage probability.