NONPARAMETRIC-TESTS FOR BOUNDS ON THE DERIVATIVE OF A REGRESSION FUNCTION

Authors
HECKMAN NE LI B
Citation
Ne. Heckman et B. Li, NONPARAMETRIC-TESTS FOR BOUNDS ON THE DERIVATIVE OF A REGRESSION FUNCTION, Annals of the Institute of Statistical Mathematics, 48(2), 1996, pp. 315-336
Citations number
6
Categorie Soggetti
Statistic & Probability",Mathematics,"Statistic & Probability
Journal title
Annals of the Institute of Statistical Mathematics → ACNP
ISSN journal
00203157
Volume
48
Issue
2
Year of publication
1996
Pages
315 - 336
Database
ISI
SICI code
0020-3157(1996)48:2<315:NFBOTD>2.0.ZU;2-K
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 b y setting k = 2 and the constant equal to zero. Our tests are based on k-th order divided difference of the observations. The asymptotic dis tribution and efficacies of these tests are computed and simulation re sults presented.