The Annals of Statistics

The Influence Function in the Errors in Variables Problem

Gabrielle Kelly

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This paper focuses on two aspects of the errors in variables problem--variance estimation of the classical estimators of slope and intercept, and the detection of influential observations. The behaviour of the jackknife, bootstrap, normal theory and influence function estimators of variability is examined under a number of sampling situations by Monte Carlo methods. In the multivariate case, perturbation analysis is used to calculate the influence function of the estimator of Gleser (1981). The connection to estimation in linear regression models is discussed. The role of the influence function in the detection of influential observations is considered and an illustration is given by a numerical example.

Article information

Ann. Statist., Volume 12, Number 1 (1984), 87-100.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62H10: Distribution of statistics
Secondary: 62E25 62J05: Linear regression

G2E20 Errors in variables multivariate structural equations model jackknife influence function bootstrap method of moments linear regression Monte Carlo outliers robust estimation


Kelly, Gabrielle. The Influence Function in the Errors in Variables Problem. Ann. Statist. 12 (1984), no. 1, 87--100. doi:10.1214/aos/1176346394.

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