## The Annals of Statistics

### 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.

#### Article information

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

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176348528

Digital Object Identifier
doi:10.1214/aos/1176348528

Mathematical Reviews number (MathSciNet)
MR1150350

Zentralblatt MATH identifier
0745.62028

JSTOR
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. https://projecteuclid.org/euclid.aos/1176348528