Empirical likelihood multiplicity adjusted estimator for multiple frame surveys

Multiple frame surveys are commonly used for a variety of reasons, including correcting for frame undercoverage, increasing the precision of estimators of population parameters for groups of interest, targeting rare populations and reducing survey costs. Several approximately design unbiased estimators have been proposed for inference from multiple frame surveys. Singh & Mecatti (2011) generalized most of the existing estimators as a class of Generalized Multiplicity-Adjusted Horvitz-Thompson Estimators. We develop an Empirical Likelihood approach to the Multiplicity-adjusted estimator. The proposed estimator allows for several multiplicity adjustments. It can handle auxiliary information and can be applied to a variety of parameters of interest expressed as unique solutions to estimating equations. Under certain sampling designs, Wilks-type confidence intervals can be calculated without variance estimates.