@article { ISI:A1996UW54700009,
title = {Nonparametric tests for bounds on the derivative of a regression function},
journal = {ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS},
volume = {48},
number = {2},
year = {1996},
month = {JUN},
pages = {315-336},
publisher = {KLUWER ACADEMIC PUBL},
type = {Article},
address = {SPUIBOULEVARD 50, PO BOX 17, 3300 AA DORDRECHT, NETHERLANDS},
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.},
keywords = {convexity, derivative of a regression function, divided differences},
issn = {0020-3157},
doi = {10.1007/BF00054793},
author = {Heckman, NE and Li, B}
}