An R Library to construct empirical likelihood confidence intervals for complex estimators

Under complex sampling designs, point estimators may not have a normal samplingdistribution and linearised variance estimators may be biased. Hence standard confidence intervals based upon the central limit theorem may have poor coverages. We propose an empirical likelihood approach which gives design based confidence intervals. The proposed approach does not rely on the normality of the point estimator, variance estimates, design-effects, re-sampling, joint-inclusion probabilities and linearisation, even when the estimator of interest is not linear. It can be used to construct confidence intervals for a large class of complex sampling designs and complex estimators which are solution of an estimating equation. It can be used for means, regressions coefficients, quantiles, totals or counts even when the population size is unknown. It can be used with large and negligible sampling fractions. It also provides asymptotically optimal point estimators, and naturally includes calibration constraints. The proposed approach is computationally simpler than the pseudo empirical likelihood and the bootstrap approaches. Berger and De La Riva Torres (2015) show that the empirical likelihood confidence interval may give better coverages than the approaches based on linearisation, bootstrap and pseudo empirical likelihood