A nonparametric test of the non-convexity of regression
- 1 January 1998
- journal article
- research article
- Published by Taylor & Francis in Journal of Nonparametric Statistics
- Vol. 9 (4) , 335-362
- https://doi.org/10.1080/10485259808832749
Abstract
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 test under the local alternatives is studied.Keywords
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This publication has 5 references indexed in Scilit:
- Comparing Nonparametric Versus Parametric Regression FitsThe Annals of Statistics, 1993
- Nonparametric Regression Tests Based on Least SquaresEconometric Theory, 1992
- Uniformly More Powerful Tests for Hypotheses Concerning Linear Inequalities and Normal MeansJournal of the American Statistical Association, 1989
- Algorithm/algorithmus 42 an algorithm for cubic spline fitting with convexity constraintsComputing, 1980
- Asymptotic Integrated Mean Square Error Using Least Squares and Bias Minimizing SplinesThe Annals of Statistics, 1980