Testing functional inequalities

By S. Lee, Kyungchul Song, Yoon-Jae Whang. 2011

74 citations recorded by the source corpus.

Abstract 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 ∞ ) . 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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9c047a8797bd9c89a30ce04f169039888cdbd52e

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES (2013, methodology): “AS compared their tests with (Chernozhukov et al., 2013, hereafter CLR) and Lee et al. (2013).”
Asymptotically exact inference in conditional moment inequality models (2011, result): “The results in this paper relate to recent work on testing conditional moment inequalities, including papers by Andrews and Shi (2009), Kim (2008), Khan and Tamer (2009), Chernozhukov, Lee, and Rosen (2009), Lee, Song, and Whang (2011), Ponomareva (2010), Menzel (2008) and Armstrong (2011).”
Nonparametric Inference Based on Conditional Moment Inequalities (2014, unknown): “As far as we are aware, the only other paper in the literature that covers the examples described above is Chernozhukov, Lee, and Rosen (2008) (CLR).”