Title: Empirical likelihood approaches under complex sampling
Authors: Yves Berger - University of Southampton (United Kingdom) [presenting]
Abstract: Data are often collected with unequal probabilities from stratified population. Empirical Likelihood is widely used in mainstream statistics. We propose a new empirical likelihood approach for sample data selected with unequal probabilities. In this situation, the standard empirical likelihood approach cannot be applied. Under a set of regularity conditions, the empirical log-likelihood function has an asymptotic chi-squared distribution. The proposed approach does not rely on variance estimates, re-sampling or joint-inclusion probabilities, even when the parameter of interest is not linear and does not have a normal distribution. An alternative approach is the pseudoempirical log-likelihood function which is not entirely appealing from a theoretical point of view, because it relies on a parameter (the design effect) which need to be estimated. A previous approach does not rely on design effect, and can be more accurate than the adjusted pseudoempirical approach. Standard confidence intervals based on variance estimates may give poor coverages, when normality does not hold. This can be the case with skewed data and outlying values. The proposed empirical likelihood confidence interval has good coverages and balanced tail errors even when the sampling distribution of the point estimator is not normal.