Consistency for least squares regression estimators with infinite variance data
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The least squares estimators are discussed for the linear regression model with random predictors. Both predictors and errors may have infinite variance. Under the condition that the predictors are in a stable domain of attraction, we determine necessary and sufficient conditions for weak consistency of the least squares estimators in the simple linear model. The conditions vary, depending on whether the intercept parameter is included in the model. We also give sufficient conditions for consistency in a multiple regression setting. 1989.