Robust penalized empirical likelihood in high dimensional longitudinal data analysis

As an effective nonparametric method, empirical likelihood (EL) is appealing in combin-ing estimating equations flexibly and adaptively for incorporating data information. To select important variables and estimating equations in a sparse high-dimensional model, a penalized EL method based on robust estimating functions is proposed for regularizing the regression parameters and the associated Lagrange multipliers simultaneously, which allows the dimensionality of both regression parameters and estimating equations to grow exponentially with the sample size. A first inspection on the robustness of estimating equations contributing to variable selection is discussed from both theoretical perspective and intuitive simulation results in this paper. 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 robustness of the estimator is measured via the bounded influence function, and the oracle properties are also established under some regularity conditions. Extensive simulation studies and yeast cell data are used to evaluate the performance of the proposed method. The numerical results reveal that the robustness of sparse estimating equations selection fundamentally enhances variable selection accuracy when the data have heavy tails and/or include underlying outliers. & COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

Empirical likelihood (EL) is an effective nonparametric method that combines estimating equations flexibly and adaptively. A penalized EL method based on robust estimating functions is proposed for variable selection in a high-dimensional model, allowing the dimensions to grow exponentially with the sample size. The proposed method improves robustness and effectiveness in the presence of outliers or heavy-tailed data. Extensive simulation studies and a real data example demonstrate the enhanced variable selection accuracy when dealing with heavy-tailed data or outliers.