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As an effective nonparametric method, empirical likelihood (EL) is appealingin combining estimating equations flexibly and adaptively for incorporatingdata information. To select important variables and estimating equations in thesparse high-dimensional model, we consider a penalized EL method based onrobust estimating functions by applying two penalty functions for regularizingthe regression parameters and the associated Lagrange multiplierssimultaneously, which allows the dimensionalities of both regression parametersand estimating equations to grow exponentially with the sample size. A firstinspection on the robustness of estimating equations contributing to theestimating equations selection and variable selection is discussed from boththeoretical perspective and intuitive simulation results in this paper. Theproposed method can improve the robustness and effectiveness when the data haveunderlying outliers or heavy tails in the response variables and/or covariates.The robustness of the estimator is measured via the bounded influence function,and the oracle properties are also established under some regularityconditions. Extensive simulation studies and a yeast cell data are used toevaluate the performance of the proposed method. The numerical results revealthat the robustness of sparse estimating equations selection fundamentallyenhances variable selection accuracy when the data have heavy tails and/orinclude underlying outliers.

Robust penalized empirical likelihood in high dimensional longitudinal data analysis