A Consistent Nonparametric Test of the Convexity of Regression Based on Least Squares Splines

Abstract

This paper provides a test of convexity of a regression function. This test is based on the least squares splines. The test statistic is shown to be asymptotically of size equal to the nominal level, while diverging to infinity if the convexity is misspecified. Therefore, the test is consistent against all deviations from the null hypothesis.