Two Stage Smoothing of Scatterplots

Abstract

Scatterplot smoothing is a simple but a very useful tool for data analysis. A smooth curve superimposed on the scatterplot greatly enhances the visual information, especially, the bivariate association between the prediction variable and the response variable. In this article some smoothers are reviewed with respect to consistency and sensitivity to discontinuities on the underlying functions. Robust centered span smoothers produce smooth and consistent curves but they tend to smooth over or blur the discontinuities. Non-centered span smoothers are sensitive to the discontinuities but they tend to be rough and lack consistency. Two stage smoothing is proposed as a technique that provides consistency as well as sensitivity to discontinuities.