Tracing the Curvature of a Regression Curve

The extended Gini regression is a semi parametric regression which allows the user to assign different weights to different sections of the explanatory variables. We illustrate, via examples, the ability of extended Gini (EG) regression to detect sections of monotonic increase or decrease, as well as convexity and concavity of (unknown) regression curves with respect to each explanatory variable separately, given the other explanatory variables. EG regression is based on using several linear approximations that differ by one parameter. The parameter enables the investigator to change the weighting scheme applied to slopes of the regression curve in a systematic way and thus follow the curvatures. The method is illustrated by two (simulated) examples. An alternative method that enables to trace the curvature is quantile regression (QR). However, for these examples QR fails to trace the curvature. A possible explanation is that while the weighting scheme of QR is applied to the residuals, the weighting scheme of EG is applied to the explanatory variable(s)