A nonparametric test of the non-convexity of regression - Cheikh A. T. Diack; Christine Thomas-Agnan (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 1998)
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 class 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 test under the local alternatives is studied.
urn:nbn:de:kobv:11-10056968
Keywords: 330; least squares estimator; test of convexity; B-splines; modulus of continuity