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Testing functional inequalities

Authors: Sokbae (Simon) Lee , Song, Kyungchul and Yoon-Jae Whang
Date: 31 January 2013
Type: Journal article, Journal of Econometrics, Vol. 172, No. 1, pp. 14--32
DOI: 10.1016/j.jeconom.2012.08.006


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:
Sokbae (Simon) Lee, Kyungchui (Kevin) Song and Yoon-Jae Whang February 2011, Testing functional inequalities, cemmap Working Paper

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