Rescaling Bootstrap Technique for Variance Estimation in Dual Frame Surveys

Abstract

In a Dual Frame (DF) surveys, set of two frames is used instead of a traditional single frame of sampling units from the target population. Dual frame surveys are applicable in those situations where one frame covers the entire population but very expensive to sample; so an alternate frame may be available that does not cover the entire population but is inexpensive to sample. As Hartley (1962) noted, variance estimation can be more complicated for dual frame surveys than for a single-frame survey. Unbiased variance estimator of parameter of interest is very tedious to obtain for estimator using dual frame surveys. In this article, we propose two rescaling bootstrap variance estimation techniques in dual frame surveys viz. Stratified Rescaling Bootstrap Without Replacement (SRBWO) and Post-stratified Rescaling Bootstrap Without Replacement (PRBWO) methods. Statistical properties of the proposed methods are compared through a simulation study. Simulation results suggest that the proposed SRBWO and PRBWO methods give an unbiased estimate of the variance of the dual frame estimator of population total and the SRBWO method performs better than the PRBWO method.