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Testing functional inequalities
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DOI：10.1016/j.jeconom.2012.08.006.png)
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Abstract
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This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of L-p-type functionals of kernel estimators (1 <= p < infinity). 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. (C) 2012 Elsevier B.V. All rights reserved.
Keywords:
Conditional moment inequalities
Kernel estimation
One-sided test
Local power
L-p norm
Poissonization
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