A0224
Title: A novel robust weighted least squares regression line
Authors: Alfonso Garcia-Perez - Universidad Nacional de Educación a Distancia (UNED) (Spain) [presenting]
Abstract: Some regression line estimators, such as least median squares (LMS) and least trimmed squares (LTS) estimators have been proposed in the literature as robust alternatives to the classical least squares LS estimators. A novel weighted least squares regression line is introduced, based on considering, as weights, the tail distribution of the studentized residuals Tn when errors in the model follow a scale-contaminated normal distribution. Until now, weights in other weighted least squares estimators are based on the squared-residuals magnitude in LS. Tn distribution is used, so the outliers with respect to Tn are less weighted because they are less likely to appear. This new regression line has some advantages, such as smooth and differentiable objective function, contrary to what happens with LMS or LTS. It also has a closed-form expression and good interesting properties. Finally, with this new regression line, a new robust inverse-variance weighted (IVW) estimator in Mendelian randomization is proposed because of the relationship between the IVW estimators and the slopes of the regression of effect on the instrumental variables Z and the regression of Cause on Z.
