RCR: Robust Compound Regression for Robust Estimation of Errors-in-Variables Model

TL;DR

This paper introduces RCR, a new robust regression method for errors-in-variables models that effectively handles outliers and measurement errors, improving estimation accuracy in applied sciences.

Contribution

The paper develops RCR, a novel nonparametric regression approach that generalizes existing methods, offering robust and flexible estimation for EIV models.

Findings

RCR outperforms traditional estimators in simulations.

RCR provides robust estimates in real-life data examples.

The method offers flexibility to optimize regression efficiency.

Abstract

The errors-in-variables (EIV) regression model, being more realistic by accounting for measurement errors in both the dependent and the independent variables, is widely adopted in applied sciences. The traditional EIV model estimators, however, can be highly biased by outliers and other departures from the underlying assumptions. In this paper, we develop a novel nonparametric regression approach - the robust compound regression (RCR) analysis method for the robust estimation of EIV models. We first introduce a robust and efficient estimator called least sine squares (LSS). Taking full advantage of both the new LSS method and the compound regression analysis method developed in our own group, we subsequently propose the RCR approach as a generalization of those two, which provides a robust counterpart of the entire class of the maximum likelihood estimation (MLE) solutions of the EIV model, in a 1-1 mapping. Technically, our approach gives users the flexibility to select from a class of RCR estimates the optimal one with a predefined regression efficiency criterion satisfied. Simulation studies and real-life examples are provided to illustrate the effectiveness of the RCR approach.