A nonparametric test of the non-convexity of regression

This paper proposes a nonparametric test of the non-convexity of a smooth regression function based on least squares or hybrid splines. By a simple formulation of the convexity hypothesis in the lcass of all polynomial cubic splines, we build a test which has an asymptotic size equal to the nominal level. It is shown that the test is consistent and is robust to nonnormality. The behavior of the lest under the local alternatives is studied.