Measurement Errors as Bad Leverage Points

TL;DR

This paper models measurement errors in linear regression as bad leverage points and demonstrates that high-breakdown estimators can effectively identify and mitigate contaminated data, improving bias and confidence intervals.

Contribution

It introduces a novel perspective on measurement errors as leverage points and shows that high-breakdown estimators can handle substantial contamination.

Findings

High-breakdown estimators reduce bias in contaminated data

Robust estimators maintain reliable confidence intervals

Effective when less than half the data is heavily contaminated

Abstract

Errors-in-variables is a long-standing, difficult issue in linear regression; and progress depends in part on new identifying assumptions. I characterize measurement error as bad-leverage points and assume that fewer than half the sample observations are heavily contaminated, in which case a high-breakdown robust estimator may be able to isolate and down weight or discard the problematic data. In simulations of simple and multiple regression where eiv affects 25% of the data and R-squared is mediocre, certain high-breakdown estimators have small bias and reliable confidence intervals.