Journal Article

Testing functional inequalities

Authors

Sokbae (Simon) Lee, Song, Kyungchul, Yoon-Jae Whang

Published Date

31 January 2013

Type

Journal Article

This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of Lp-type functionals of kernel estimators (1≤p<∞). Drawing on the approach of Poissonization, this paper establishes that the tests are asymptotically distribution free, admitting asymptotic normal approximation. In particular, the tests using the standard normal critical values have asymptotically correct size and are consistent against general fixed alternatives. Furthermore, we establish conditions under which the tests have nontrivial local power against Pitman local alternatives. Some results from Monte Carlo simulations are presented.


Previous version

Testing functional inequalities
Sokbae (Simon) Lee, Kyungchui (Kevin) Song, Yoon-Jae Whang
CWP12/11