High-dimensional outlier detection and variable selection via adaptive weighted mean regression

TL;DR

This paper introduces an adaptive weighted mean regression method that robustly detects outliers and selects variables in high-dimensional data, effectively handling heavy-tailed and heteroscedastic errors.

Contribution

It develops a novel adaptive penalized weighted mean regression framework with theoretical guarantees for outlier detection and variable selection in high-dimensional models.

Findings

Demonstrates robustness against outliers in response and covariates

Achieves oracle inequalities and consistency in outlier detection

Performs well in simulations and real data, outperforming existing methods

Abstract

This paper proposes an adaptive penalized weighted mean regression for outlier detection of high-dimensional data. In comparison to existing approaches based on the mean shift model, the proposed estimators demonstrate robustness against outliers present in both response variables and/or covariates. By utilizing the adaptive Huber loss function, the proposed method is effective in high-dimensional linear models characterized by heavy-tailed and heteroscedastic error distributions. The proposed framework enables simultaneous and collaborative estimation of regression parameters and outlier detection. Under regularity conditions, outlier detection consistency and oracle inequalities of robust estimates in high-dimensional settings are established. Additionally, theoretical robustness properties, such as the breakdown point and a smoothed limiting influence function, are ascertained. Extensive simulation studies and a breast cancer survival data are used to evaluate the numerical performance of the proposed method, demonstrating comparable or superior variable selection and outlier detection capabilities.