Empirical likelihood confidence intervals and significance test for regression parameters under complex sampling designs

Abstract

Confidence intervals based on ordinary least squares may have poor coverages for regression parameters when the effect of sampling design is ignored. Standard confidence intervals based on design variances may not have the right coverages when the sampling distribution is skewed. Berger and De La Riva Torres (2012) proposed an empirical likelihood approach which can be used for point estimation and to construct confidence intervals under complex sampling designs for a single parameter. We show that this approach can be extended to test the significance of a subset of model parameters and to derive confidence intervals. The proposed approach is not a straightforward extension of Berger and De La Riva Torres (2012) approach, because we consider the situation when the parameter is multidimensional and the parameter of interest is a subset of the parameter. This requires profiling which is not covered by Berger and De La Riva Torres (2012). The proposed approach intrinsically incorporates sampling weights, design variables, and auxiliary information. It may yield to more accurate confidence intervals when the sampling distribution of the regression parameters is not normal, the point estimator is biased, or the regression model is not linear. The proposed approach is simple to implement and less computer intensive than bootstrap. The proposed approach does not rely on re-sampling, linearisation, variance estimation, or design-effect