Comparing Recent Approaches For Bootstrapping Sample Survey Data: A First Step Towards A Unified Approach

Bootstrap algorithms are simple and appealing solutions for variance estimation under a complex sampling design, however, they must account for the non-iid nature of data. Literature about boot- strapping finite population samples appears to have developed according to two major approaches. A more practical ad-hoc approach refers to the so-called scaling problem and is based on a data- rescaling so that, in the linear case, the resulting bootstrap estimate for the variance perfectly matches the analytic variance estimate. A more fundamental plug-in approach is based on the mim- icking bootstrap principle and on the bootstrap population created on the basis of (original) sample data. Recent proposals suggest a direct bootstrap matching the linear case variance but avoiding any data scaling under mixed re-sampling designs. In this paper, a new perspective to the bootstrap population plug-in approach is provided that avoids the physical reconstruction of the bootstrap population. Basic sampling designs, both with and without replacement as well as unequal proba- bility designs are considered. Focusing on probability-proportional-to-size sampling, a simulation study is conducted that compares all the approaches considered.