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Nonparametric tests for bounds on the derivative of a regression function

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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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Authors and Affiliations

  1. Statistics Department, University of British Columbia, V6T 1Z2, Vancouver, BC, Canada

    Nancy E. Heckman

  2. Statistics Department, Pennsylvania State University, 16802, University Park, PA, U.S.A.

    Bing Li

Authors
  1. Nancy E. Heckman
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  2. Bing Li
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Additional information

Research supported by Natural Sciences and Engineering Research Council of Canada Grant OGP0007969.

Research supported by National Science Foundation Grant DMS-9306738.

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Heckman, N.E., Li, B. Nonparametric tests for bounds on the derivative of a regression function. Ann Inst Stat Math 48, 315–336 (1996). https://doi.org/10.1007/BF00054793

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  • DOI: https://doi.org/10.1007/BF00054793

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