RCR: Robust Compound Regression for Robust Estimation of Errors-in-Variables Model
This work addresses robustness issues in errors-in-variables models for applied sciences, representing an incremental improvement by combining and extending existing methods.
The paper tackles the problem of bias in errors-in-variables regression models due to outliers by developing a robust compound regression (RCR) method, which generalizes existing techniques to provide robust maximum likelihood estimation solutions with flexibility for optimal selection based on efficiency criteria, as demonstrated through simulation studies and real-life examples.
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.