### Abstract

We consider two tests of the null hypothesis that the k-th derivative of a regression function is uniformly bounded by a specified constant. These tests can be used to study the shape of the regression function. For instance, we can test for convexity of the regression function by setting k = 2 and the constant equal to zero. Our tests are based on k-th order divided difference of the observations. The asymptotic distribution and efficacies of these tests are computed and simulation results presented.

Original language | English (US) |
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Pages (from-to) | 315-336 |

Number of pages | 22 |

Journal | Annals of the Institute of Statistical Mathematics |

Volume | 48 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1996 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability

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## Cite this

Heckman, N. E., & Li, B. (1996). Nonparametric tests for bounds on the derivative of a regression function.

*Annals of the Institute of Statistical Mathematics*,*48*(2), 315-336. https://doi.org/10.1007/BF00054793