Open Access
March, 1992 Generalized $M$-Estimators for Errors-in-Variables Regression
Chi-Lun Cheng, John W. Van Ness
Ann. Statist. 20(1): 385-397 (March, 1992). DOI: 10.1214/aos/1176348528


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.


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Chi-Lun Cheng. John W. Van Ness. "Generalized $M$-Estimators for Errors-in-Variables Regression." Ann. Statist. 20 (1) 385 - 397, March, 1992.


Published: March, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0745.62028
MathSciNet: MR1150350
Digital Object Identifier: 10.1214/aos/1176348528

Primary: 62F35
Secondary: 62J05

Keywords: errors-in-variables regression , Fisher consistency , generalized $M$-estimates , measurement error model , robust statistics , structural model

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 1 • March, 1992
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