Penalised Empirical likelihood approach for parameters which are solutions of estimating equations Seminar

Abstract
The sampling fraction is defined as the ratio between the sample size n and the population size N. In mainstream statistics, the sample can be considered as a set of independent and identically distributed (iid) observations from an infinite population. Usually, it is assumed that n/N tends to zero. However, for business surveys, it is not uncommon to use large sampling fractions. In this case the sample is a non-negligible subset of a population, and n/N is not negligible. We consider an asymptotic framework where n and N tends to infinity, and n/N is bounded away from zero. We propose a penalised empirical likelihood approach which can be used for large sampling fractions. We show how this approach can be used for point estimation, testing and for confidence intervals. The class of parameters of interest considered are solutions of estimating equations; such as means, regressions coefficients, quantiles and totals. Confidence intervals can be calculated without the need of variance estimates, design-effects, re-sampling (i.e. bootstrap or jackknife), joint-inclusion probabilities and linearisation, even when the estimator of interest is not linear. The proposed approach does not rely on the normality of the point estimator. This is non-parametric approach, as it does not rely on assumption about the distribution for the variable of interest. The proposed approach also takes into account of other characteristics such as stratification, unequal probabilities of selection and calibration (side information or population level information). The simulation study shows that the proposed approach penalised empirical likelihood approach may give better coverages than the confidence intervals based on linearisation, bootstrap and pseudo empirical likelihood. We also present a numerical illustration based on the European Survey on Income and Living Conditions (EU-SILC).