Generalized $M$-Estimators for Errors-in-Variables Regression

Abstract

This paper discusses robust estimation for structural errors-in-variables (EV) linear regression models. Such models have important applications in many areas. Under certain assumptions, including normality, the maximum likelihood estimates for the EV model are provided by orthogonal regression (OR) which minimizes the orthogonal distance from the regression line to the data points instead of the vertical distance used in ordinary regression. OR is very sensitive to contamination and thus efficient robust procedures are needed. This paper examines the theoretical properties of bounded influence estimators for univariate Gaussian EV models using a generalized $M$-estimate approach. The results include Fisher consistency, most $B$-robust estimators and the OR version of Hampel's optimality problem.