Empirical likelihood approach for estimation from multiple sources

Empirical likelihood is a non-parametric, likelihood-based inference approach. In the design-based empirical likelihood approach introduced by Berger and De La Riva Torres (2016), the parameter of interest is expressed as a solution to an estimating equation. The maximum empirical likelihood point estimator is obtained by maximising the empirical likelihood function under a system of constraints. A single vector of weights, which can be used to estimate various parameters, is created. Design-based empirical likelihood confidence intervals are based on the χ2 approximation of the empirical likelihood ratio function. The confidence intervals are range-preserving and asymmetric, with the shape driven by the distribution of the data. In this thesis we focus on the extension and application of design-based empirical likelihood methods to various problems occurring in survey inference. First, a design-based empirical likelihood methodology for parameter estimation in two surveys context, in presence of alignment and benchmark constraints, is developed. Second, a design-based empirical likelihood multiplicity adjusted estimator for multiple frame surveys is proposed. Third, design-based empirical likelihood is applied to a practical problem of census coverage estimation. The main contribution of this thesis is defining the empirical likelihood methodology for the studied problems and showing that the aligned and multiplicity adjusted empirical likelihood estimators are √n-design-consistent. We also discuss how the original proofs presented by Berger and De La Riva Torres (2016) can be adjusted to show that the empirical likelihood ratio statistic is pivotal and follows a χ2 distribution under alignment constraints and when the multiplicity adjustments are used. We evaluate the asymptotic performance of the empirical likelihood estimators in a series of simulations on real and artificial data. We also discuss the computational aspects of the calculations necessary to obtain empirical likelihood point estimates and confidence intervals and propose a practical way to obtain empirical likelihood confidence intervals in situations when they might be difficult to obtain using standard approaches.