On simultaneously identifying outliers and heteroscedasticity without specific form

Assuming homogeneous variance in a normal regression model is not always appropriate as invalid standard inference procedures may result from the improper estimation of the standard error when the disturbance process in a regression model presents heteroscedasticity. When both outliers and heteroscedasticity exist, the inflation of the scale’s estimate can deteriorate. Using graphical analysis, this study identifies outliers under heteroscedastic error without specifying a functional form. A jigsaw plot with two kinds of cut-off points differentiates both outlying and heteroscedastic characteristics for each observation in the data. The proposed approach is based on the concept of the weighted least absolute deviation estimator. Furthermore, plugging the resulting residuals into the estimation of the heteroscedasticity-consistent covariance matrix leads to a robust quasi-t test for the estimated coefficients.