The Annals of Statistics

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

Chi-Lun Cheng and John W. Van Ness

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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.

Article information

Ann. Statist., Volume 20, Number 1 (1992), 385-397.

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


Primary: 62F35: Robustness and adaptive procedures
Secondary: 62J05: Linear regression

Errors-in-variables regression measurement error model structural model robust statistics Fisher consistency generalized $M$-estimates


Cheng, Chi-Lun; Ness, John W. Van. Generalized $M$-Estimators for Errors-in-Variables Regression. Ann. Statist. 20 (1992), no. 1, 385--397. doi:10.1214/aos/1176348528.

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