Some Exploratory Methods for Studying Curvature in Robust Regression

The paper suggests an exploratory method for studying curvature, within the context of robust regression, using an analog of the approached developed by Doksum and Samarov (1995). The strategy begins by approximating the regression surface using a proposed generalization of the so‐called running interval smoother. The generalization consists of estimating the span via arobust measure of scale associated with the residuals. This approximation can then be used to measure linearity using a robust analog of a measure considered by Doksum and Samarov. The results are illustrated with data from a study on predicting reading ability.