Least median of squares regression and minimum volume ellipsoid estimator for outliers detection in housing appraisal

In the real estate sector the regression analysis is the most used method for interpretative and predictive purposes. However, the presence of outliers in the estimative sample can lead to ordinary last squared regression models that do not represent the investigated market phenomenon, with the consequence of producing unreliable assessments. In the present research the issue of the identification and the removal of outliers is discussed. The outliers identified by the least median of squares regression (LMS) and the minimum volume ellipsoid estimator (MVE) are compared in order to test the coincidence or the diversity. A complete diagnosis of the data of the initial estimative sample is carried out, combining the robust residuals obtained with LMS and the robust distances obtained with MVE. The data are classified into regular observations, vertical outliers, good leverage points and bad leverage points, and cases to delete and those to keep in the sample are identified.