Testing functional inequalities |
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Authors: | Sokbae Lee Kyungchul Song Yoon-Jae Whang |
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Institution: | 1. Department of Economics, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 151-742, Republic of Korea;2. Centre for Microdata Methods and Practice, Institute for Fiscal Studies, 7 Ridgmount Street, London, WC1E 7AE, UK;3. Department of Economics, University of British Columbia, 997 - 1873 East Mall, Vancouver, BC, V6T 1Z1, Canada |
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Abstract: | 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. |
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Keywords: | C12 C14 |
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