Local independence feature screening for nonparametric and semiparametric models by marginal empirical likelihood

TL;DR

This paper introduces a nonparametric, model-free feature screening method using local empirical likelihood to identify variables contributing to responses in high-dimensional data, effective even when models are unspecified.

Contribution

It proposes a novel local independence screening technique based on empirical likelihood that works for a wide range of nonparametric and semiparametric models without requiring estimation.

Findings

Method handles exponentially growing data dimensions.

Performs well in numerical experiments.

Theoretically justified for high-dimensional settings.

Abstract

We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the underlying data model, our approach accommodates a wide spectrum of nonparametric and semiparametric model families. To detect the local contributions of explanatory variables, our approach constructs empirical likelihood locally in conjunction with marginal nonparametric regressions. Since our approach actually requires no estimation, it is advantageous in scenarios such as the single-index models where even specification and identification of a marginal model is an issue. By automatically incorporating the level of variation of the nonparametric regression and directly assessing the strength of data evidence supporting local contribution from each explanatory variable, our approach provides a unique perspective for solving feature screening problems. Theoretical analysis shows that our approach can handle data dimensionality growing exponentially with the sample size. With extensive theoretical illustrations and numerical examples, we show that the local independence screening approach performs promisingly.