Nonparametric tests for bounds on the derivative of a regression function

Nancy E. Heckman; Bing Li

doi:10.1007/BF00054793

Nonparametric tests for bounds on the derivative of a regression function

Nancy E. Heckman
, Bing Li

Statistics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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)
Pages (from-to)	315-336
Number of pages	22
Journal	Annals of the Institute of Statistical Mathematics
Volume	48
Issue number	2
DOIs	https://doi.org/10.1007/BF00054793
State	Published - 1996

All Science Journal Classification (ASJC) codes

Statistics and Probability

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10.1007/BF00054793

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title = "Nonparametric tests for bounds on the derivative of a regression function",

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.",

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

AU - Heckman, Nancy E.

AU - Li, Bing

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Y1 - 1996

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.

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UR - https://www.scopus.com/pages/publications/0030353241#tab=citedBy

U2 - 10.1007/BF00054793

DO - 10.1007/BF00054793

M3 - Article

AN - SCOPUS:0030353241

SN - 0020-3157

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JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

IS - 2

ER -

Nonparametric tests for bounds on the derivative of a regression function

Abstract

All Science Journal Classification (ASJC) codes

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