Pseudo–Empirical Likelihood Inference for Multiple Frame Surveys

Abstract

This article presents a pseudo–empirical likelihood approach to inference for multiple-frame surveys. We establish a unified framework for point and interval estimation of finite population parameters, and show that inferences on the parameters of interest making effective use of different types of auxiliary population information can be conveniently carried out through the constrained maximization of the pseudo–empirical likelihood function. Confidence intervals are constructed using either the asymptotic χ2 distribution of an adjusted pseudo–empirical likelihood ratio statistic or a bootstrap calibration method. Simulation results based on Statistics Canada’s Family Expenditure Survey data show that the proposed methods perform well in finite samples for both point and interval estimation. In particular, a multiplicity-based pseudo–empirical likelihood method is proposed. This method is easily used for multiple-frame surveys with more than two frames and does not require complete frame membership information. The proposed pseudo–empirical likelihood ratio confidence intervals have a clear advantage over the conventional normal approximation–based intervals in estimating population proportions of rare items, a scenario that often motivates the use of multiple-frame surveys. All related computational problems can be handled using existing algorithms for pseudo–empirical likelihood methods with single-frame surveys.