Robust Possibility Regression

Abstract

Traditional possibility regression is not robust against outliers. To overcome this difficulty, a new methodology is proposed : the difference in intercepts of two parallel lines is minimized under the condition that a certain number of data are located between the two lines. This nonlinear regression method, featuring simple implementation and easy interpretation, does not require assumptions concerning the rate of outliers in data. Furthermore, a slight modification of this procedure leads to robust LOWESS(LOcally WEighted Scatter plot Smoothing) based on possibility regression.