Empirical likelihood based inference under complex sampling designs

Abstract

The approach proposed gives design-consistent estimators of parameters which are solutions of estimating equations (e.g. averages, totals, quantiles, correlation, (non)linear regression parameters). It can be used to construct confidence intervals without variance estimates. These confidence intervals are not based on the normality of the point estimator. Linearisation, re-sampling (jackknife or bootstrap) or joint-inclusion probabilities are not necessary, even when the parameter of interest is not linear. This approach gives consistent confidence intervals even when the sampling distribution is skewed (e.g. with domains or with outlying values), or when linearisation gives biased variance estimates. The proposed approach can be used to estimate generalised regression parameters (e.g. logistic regression) and to test if they are significant, under a design-based approach. The auxiliary information is naturally taken into account, without the need of a calibration distance function. The empirical likelihood approach is a design-based approach. A super-population model is not necessary. The empirical likelihood approach proposed is different from the pseudoempirical likelihood approach

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ORCID for Yves G. Berger: orcid.org/0000-0002-9128-5384

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