Nonparametric tests for bounds on the derivative of a regression function

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Nonparametric tests for bounds on the derivative of a regression function

TitleNonparametric tests for bounds on the derivative of a regression function
Publication TypeJournal Article
Year of Publication1996
AuthorsHeckman, NE, Li, B
JournalANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
Volume48
Pagination315-336
Date PublishedJUN
Type of ArticleArticle
ISSN0020-3157
Keywordsconvexity, derivative of a regression function, divided differences
AbstractWe 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.
DOI10.1007/BF00054793