Conditional SIRS for nonparametric and semiparametric models by marginal empirical likelihood

Dimension reduction is a crucial issue for high-dimensional data analysis. When the correlation among the variables is strong, the original SIRS (Zhu et al. in J Am Stat Assoc 106(496):1464–1475, 2011) may lose efficiency. Under high-dimensional setting, eliminating the bad influence caused by the correlation has become an important issue. Aiming at this issue, we propose a feature screening approach by combining the marginal empirical likelihood with the conditional SIRS. Based on a centralized SIRS, the correlation among the variables is significantly reduced and consequently, the related empirical likelihood is improved remarkably. Moreover, our method is model-free due to the properties of SIRS and empirical likelihood. The proposed method can select important predictors directly without parameter estimation, implying that the method is computationally simple. Under some general conditions, the proposed marginal empirical likelihood ratio is self-studentized. The simulation study shows that compared with other unconditional and conditional methods, our method is competitive and has a great superiority.

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