Rescaling bootstrap variance estimation technique under dual frame surveys with unknown domain sizes

Abstract

Dual frame (DF) surveys are a special case of multiple frame (MF) surveys considering two frames covering the entire population. Dual frame surveys are applicable in those situations, where, one frame may cover the entire population but is very expensive to sample; so an alternate frame may be available that does not cover the entire population but is easily available. Unbiased variance estimation in dual frame surveys can be difficult and complicated than corresponding estimators under single frame surveys. Again, the variance of dual frame estimator involves population variances of the individual domains which are generally unknown. Due to this reason, obtaining an unbiased estimate of the variance of the dual frame estimator is quite complex in the case of dual frame surveys. In this article, we propose a Post-stratified Rescaling Bootstrap with Unknown Domain size (PstRBUD) method for variance estimation of the dual frame estimator of population total. The proposed rescaled bootstrap method was compared to that of standard bootstrap methods in simulation analysis. The proposed PstRBUD method provides an unbiased estimation of the variance of the dual frame estimator of population total, according to simulation results.