A model-free Screening procedure

TL;DR

This paper introduces a versatile, model-free screening method for selecting relevant explanatory variables without assumptions on data distribution or model structure, supported by theoretical guarantees and empirical validation.

Contribution

It presents a novel, model-free screening procedure with proven theoretical properties, applicable across diverse situations without relying on specific model assumptions.

Findings

The method achieves the Sure Screening Property.

It effectively controls the False Positive Rate.

Validated through simulations and real data examples.

Abstract

In this article, we propose a generic screening method for selecting explanatory variables correlated with the response variable Y . We make no assumptions about the existence of a model that could link Y with a subset of explanatory variables, nor about the distribution of the variables. Our procedure can therefore be described as ''model-free'' and can be applied in a wide range of situations. In order to obtain precise theoretical guarantees (Sure Screening Property and control of the False Positive Rate), we establish a Berry-Esseen type inequality for the studentized statistic of the slope estimator. We illustrate our selection procedure using two simulated examples and a real data set.