Least trimmed squares regression with missing values and cellwise outliers

2026-03-04

AI Summary

This study addresses the limitations of traditional regression methods in simultaneously handling case-wise and cell-wise outliers as well as missing data, particularly under skewed distributions where out-of-sample prediction performance often deteriorates. To overcome these challenges, the authors propose a novel robust regression approach built upon the Least Trimmed Squares (LTS) framework. This method is the first to provide a theoretical breakdown point guarantee against cell-wise contamination and incorporates an embedded imputation mechanism tailored for asymmetric data distributions. Empirical evaluations demonstrate that the proposed technique substantially enhances both robustness and predictive accuracy in complex scenarios where outliers and missing values coexist.

Abstract

Regression is the workhorse of statistics, and is often faced with real data that contain outliers. When these are casewise outliers, that is, cases that are entirely wrong or belong to a different population, the issue can be remedied by existing casewise robust regression methods. It is another matter when cellwise outliers occur, that is, suspicious individual entries in the data matrix containing the regressors and the response. We propose a new regression method that is robust to both casewise and cellwise outliers, and handles missing values as well. Its construction allows for skewed distributions. We show that it obeys the first breakdown result for cellwise robust regression. It is also the first such method that is geared to making robust out-of-sample predictions. Its performance is studied by simulation, and it is illustrated on a substantial real dataset.

Problem

• regression
• cellwise outliers
• casewise outliers
• missing values
• robust prediction

Innovation

• least trimmed squares
• cellwise outliers
• robust regression
• missing values
• out-of-sample prediction