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The errors-in-variables (EIV) regression model, being more realistic byaccounting for measurement errors in both the dependent and the independentvariables, is widely adopted in applied sciences. The traditional EIV modelestimators, however, can be highly biased by outliers and other departures fromthe underlying assumptions. In this paper, we develop a novel nonparametricregression approach - the robust compound regression (RCR) analysis method forthe robust estimation of EIV models. We first introduce a robust and efficientestimator called least sine squares (LSS). Taking full advantage of both thenew LSS method and the compound regression analysis method developed in our owngroup, we subsequently propose the RCR approach as a generalization of thosetwo, which provides a robust counterpart of the entire class of the maximumlikelihood estimation (MLE) solutions of the EIV model, in a 1-1 mapping.Technically, our approach gives users the flexibility to select from a class ofRCR estimates the optimal one with a predefined regression efficiency criterionsatisfied. Simulation studies and real-life examples are provided to illustratethe effectiveness of the RCR approach.

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