Abstract
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.
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