Abstract:
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This paper provides a comprehensive treatment on design-based empirical likelihood inferences for complex surveys with estimating equations. Our settings are very general: (i) The estimating functions can be smooth or non-differentiable, covering descriptive population parameters, linear and generalized linear models, population quantiles as well as quantile regression models; and (ii) The dimension of the estimating functions can be higher than the dimension of the parameters, allowing additional calibration constraints. Our theoretical results have two prominent features: (a) Asymptotic distributions of the empirical likelihood ratio statistics are derived for arbitrary sampling designs, with simplified results presented for single-stage unequal probability sampling; and (b) Empirical likelihood ratio tests for general linear or nonlinear hypotheses are developed for model building, and a penalized empirical likelihood method is proposed for design-based variable selection with oracle properties. Finite sample performances of our proposed methods are examined through simulation studies and a real survey data set is used to test the method for variable selection.
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