### 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 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability

### Cite this

*Annals of the Institute of Statistical Mathematics*,

*48*(2), 315-336. https://doi.org/10.1007/BF00054793

}

*Annals of the Institute of Statistical Mathematics*, vol. 48, no. 2, pp. 315-336. https://doi.org/10.1007/BF00054793

**Nonparametric tests for bounds on the derivative of a regression function.** / Heckman, Nancy E.; Li, Bing.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Nonparametric tests for bounds on the derivative of a regression function

AU - Heckman, Nancy E.

AU - Li, Bing

PY - 1996/1/1

Y1 - 1996/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0030353241&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030353241&partnerID=8YFLogxK

U2 - 10.1007/BF00054793

DO - 10.1007/BF00054793

M3 - Article

VL - 48

SP - 315

EP - 336

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 2

ER -