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Biometrika 1981 68(1):21-33; doi:10.1093/biomet/68.1.21
© 1981 by Biometrika Trust
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On the estimation of slope and the identification of outliers in linear regression

R. L. CHAMBERS and C. R. HEATHCOTE

Australian Bureau of Statistics Canberra
Department of Statistics, Australian National University Canberra

The paper presents a large sample method for estimating the slope parameter in a linear model by minimizing a loss function related to the empirical cumulant generating function of the error distribution. A family of estimators, indexed by a real parameter, is obtained and consistency and asymptotic normality established. The optimum member of the family is that which has minimum variance with respect to the parameter. This minimization together with a characterization result for the normal distribution leads to a procedure for the identification of outliers with respect to least squares.

Key Words: Linear regression • Long-tailed errors • Outlier detection • Robust estimation


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