Abstract: The sample empirical likelihood approach provides a powerful tool for the analysis of complex survey data. We present sample empirical likelihood results for point estimation and linear or nonlinear hypothesis tests on finite population parameters. These parameters are defined using just-identified or over-identified estimating equation systems with smooth or nondifferentiable estimating functions under general unequal probability sampling designs. We propose a penalized sample empirical likelihood for variable selection and establish its oracle property under the design-based framework. Practical implementations of the methods are also discussed. We investigate the finite sample performances of the proposed methods for quantile regression and variable selection using simulation studies. Lastly, we apply these methods to a survey data set from the International Tobacco Control (ITC) Policy Evaluation Project to demonstrate the effectiveness of the variable selection method for linear and quantile regression models.

Key words and phrases: Design-based variable selection theory, general hypothesis test, non-differentiable estimating functions, over-identified estimating equation system, quantile regression analysis, unequal probability sampling.