The Annals of Statistics

The Influence Function in the Errors in Variables Problem

Gabrielle Kelly

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Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346394

Digital Object Identifier
doi:10.1214/aos/1176346394

Mathematical Reviews number (MathSciNet)
MR733501

Zentralblatt MATH identifier
0558.62065

JSTOR
links.jstor.org

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

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

Citation

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


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