We develop an empirical likelihood (EL) inference on parameters in generalized estimating equations with nonignorably missing response data. We consider an exponential tilting model for the nonignorably missing mechanism, and propose modified estimating equations by imputing missing data through a kernel regression method. We establish some asymptotic properties of the EL estimators of the unknown parameters under different scenarios. With the use of auxiliary information, the EL estimators are statistically more efficient. Simulation studies are used to assess the finite sample performance of our proposed EL estimators. We apply our EL estimators to investigate a data set on earnings obtained from the New York Social Indicators Survey.
Summary We propose a Bayesian empirical likelihood approach to survey data analysis on a vector of finite population parameters defined through estimating equations. Our method allows overidentified estimating equation systems and is applicable to both smooth and non‐differentiable estimating functions. Our proposed Bayesian estimator is design consistent for general sampling designs and the Bayesian credible intervals are calibrated in the sense of having asymptotically valid design‐based frequentist properties under single‐stage unequal probability sampling designs with small sampling fractions. Large sample properties of the Bayesian inference proposed are established for both non‐informative and informative priors under the design‐based framework. We also propose a Bayesian model selection procedure with complex survey data and show that it works for general sampling designs. An efficient Markov chain Monte Carlo procedure is described for the required computation of the posterior distribution for general vector parameters. Simulation studies and an application to a real survey data set are included to examine the finite sample performances of the methods proposed as well as the effect of different types of prior and different types of sampling design.
Summary This paper provides an overview on two parallel approaches to design‐based inference with complex survey data: the pseudo empirical likelihood methods and the sample empirical likelihood methods. The general framework covers parameters defined through smooth or non‐differentiable estimating functions for analytic use of survey data as well as descriptive finite population parameters, and the theory focuses on point estimation, hypothesis tests and variable selection under an arbitrary sampling design. Major practical issues for the implementation of the methods, including computational algorithms, are briefly discussed. Results from simulation studies to compare the finite sample performances of the two approaches are presented.
Public-use survey data are an important source of information for researchers in social science and health studies to build statistical models and make inferences on the target finite population. This paper presents two general inferential tools through the pseudo empirical likelihood and the sample empirical likelihood methods. Theoretical results on point estimation and linear or nonlinear hypothesis tests involving parameters defined through estimating equations are established, and practical issues with the implementation of the proposed methods are discussed. Results from simulation studies and an application to the 2016 General Social Survey dataset of Statistics Canada show that the proposed methods work well under different scenarios. The inferential procedures and theoretical results presented in the paper make the empirical likelihood a practically useful tool for users of complex survey data.
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