Comparing Recent Approaches for Bootstrapping Sample Survey Data: A First Step Toward 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 bootstrapping 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 mimicking 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 probability designs are considered. Focusing on probability-proportional-to-size sampling, a simulation study is conducted that compares all the approaches considered.