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 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. 1 key words:least squares estimator, test of convexity, B-splines, modulus of continuity 1 INTRODUCTION This paper proposes a test of non-convexity of an unknown regression function in a nonparametric regression model. Interest in this problem which has been addressed for example in Schlee(1980) and Yatchew(1992), arises in particular from econometric models. Economic theory predicts the convexity of functions like for example cost functions, production functions, Engel curves... Such tests provide a way of confronting theory with real data sets. ..