With-replacement bootstrap variance estimation for household surveys: principles, examples and implementation

Variance estimation is a challenging problem in surveys, for which bootstrap is an important tool. In this work, we are interested in the use of the with-replacement bootstrap for household surveys, with or without sub-sampling of individuals. We make explicit the benchmark variance estimators that the with-replacement bootstrap aims at reproducing. We also explain how the with-replacement bootstrap can be used for sampling, treatment of unit non-response and calibration. For clarity, the proposed methods are illustrated on a running example. They are evaluated through a simulation study, and applied to a French Panel for Urban Policy. Two SAS macros to perform the bootstrap methods are also developed.