Robust penalized empirical likelihood in high dimensional longitudinal data analysis

As an effective nonparametric method, empirical likelihood (EL) is appealing in combining estimating equations flexibly and adaptively for incorporating data information. To select important variables in the sparse high-dimensional model, we consider a penalized EL method based on robust estimating functions by applying two penalty functions for regularizing the regression parameters and the associated Lagrange multipliers simultaneously, which allows the dimensionalities of both regression parameters and estimating equations to grow exponentially with the sample size. The proposed method can improve the robustness and effectiveness when the data have underlying outliers or heavy tails in the response variables and/or covariates. The oracle properties are also established under some regularity conditions. Extensive simulation studies and a yeast cell data are used to evaluate the performance of the proposed method. The numerical results reveal that robust remedies on estimating equations are needed when the data have heavy tails and/or include underlying outliers.