Robust Variable Selection for High-dimensional Regression with Missing Data and Measurement Errors

TL;DR

This paper introduces a robust variable selection method for high-dimensional regression with missing data and measurement errors, using an exponential loss function and inverse probability weighting to improve accuracy and robustness.

Contribution

It proposes a novel exponential loss function with a tuning parameter and the Atan penalty, enhancing robustness in variable selection under data imperfections.

Findings

The method improves variable selection accuracy in simulations.

It performs well on real breast cancer data.

The Atan penalty outperforms traditional penalties.

Abstract

In our paper, we focus on robust variable selection for missing data and measurement error. Missing data and measurement errors can lead to confusing data distribution. We propose an exponential loss function with a tuning parameter to apply to Missing and measurement errors data. By adjusting the parameter, the loss function can be better and more robust under various data distributions. We use inverse probability weighting and additive error models to address missing data and measurement errors. Also, we find that the Atan punishment method works better. We used Monte Carlo simulations to assess the validity of robust variable selection and validated our findings with the breast cancer dataset.