|Date:||Thursday, October 12, 2017|
In the absence of non-response, a class of bootstrap procedures consists of first creating a pseudo-population from the original sample. Bootstrap samples are then selected from this pseudo-population using the same sampling design utilized to select the original samples; see Booth et al. (1994), Holmberg (1998) and Chauvet (2007), among others. In the context of non-respondents, we develop pseudo-population type bootstrap procedures that can be used even for large sampling fractions to estimate the variance of an imputed estimator. These procedures can be applied to a large class of sampling designs, namely the class of high entropy sampling designs (Berger, 1998, 2011), that includes the Poisson sampling design, the conditional Poisson sampling design (Hàjek, 1964) and the Rao-Sampford design (Rao, 1965; Sampford, 1967). We present two bootstrap schemes: the first leads to a consistent bootstrap variance estimator with respect to the non-response model approach and the second leads to a consistent bootstrap variance estimator with respect to the imputation model approach.