Nonparametric tests for bounds on the derivative of a regression function

Nancy E. Heckman, Bing Li

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish (US)
Pages (from-to)315-336
Number of pages22
JournalAnnals of the Institute of Statistical Mathematics
Issue number2
StatePublished - 1996

All Science Journal Classification (ASJC) codes

  • Statistics and Probability


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