Nonparametric tests for bounds on the derivative of a regression function

Nancy E. Heckman, Bing Li

Research output: Contribution to journalArticle

3 Citations (Scopus)

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) 315-336 22 Annals of the Institute of Statistical Mathematics 48 2 https://doi.org/10.1007/BF00054793 Published - Jan 1 1996

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Non-parametric test
Regression Function
Derivative
Divided Differences
Null hypothesis
Asymptotic distribution
Convexity
Efficacy
Zero
Simulation

All Science Journal Classification (ASJC) codes

• Statistics and Probability

Cite this

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In: Annals of the Institute of Statistical Mathematics, Vol. 48, No. 2, 01.01.1996, p. 315-336.

Research output: Contribution to journalArticle

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AU - Li, Bing

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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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