TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES

By S. Lee, Kyungchul Song, Yoon-Jae Whang. Econometric Theory, 2013

54 citations recorded by the source corpus.

In this article, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a unified framework, with a number of possible applications in auction models, game theoretic models, wage inequality, and revealed preferences. Our test involves a one-sided version of Lp functionals of kernel-type estimators (1 ≤ p < ∞) and is easy to implement in general, mainly due to its recourse to the bootstrap method. The bootstrap procedure is based on the nonparametric bootstrap applied to kernel-based test statistics, with an option of estimating “contact sets.” We provide regularity conditions under which the bootstrap test is asymptotically valid uniformly over a large class of distributions, including cases where the limiting distribution of the test statistic is degenerate. Our bootstrap test is shown to exhibit good power properties in Monte Carlo experiments, and we provide a general form of the local power function. As an illustration, we consider testing implications from auction theory, provide primitive conditions for our test, and demonstrate its usefulness by applying our test to real data. We supplement this example with the second empirical illustration in the context of wage inequality.

Subfields: Economics and Econometrics, Management Science and Operations Research, Marketing

View Paper: https://www.semanticscholar.org/paper/2c7ee11c9087b53f4000aa1d0e242a6ae7b68762

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In Economics and Econometrics

1. D. Wilhelm
2. D. Chetverikov
3. Kengo Kato
4. Victor Chernozhukov
5. T. Armstrong

In Management Science and Operations Research

1. D. Wilhelm
2. D. Chetverikov
3. Victor Chernozhukov
4. Kengo Kato
5. T. Armstrong

In Marketing

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2. D. Chetverikov
3. Victor Chernozhukov
4. Kengo Kato
5. T. Armstrong

Citations in the corpus

• TESTING REGRESSION MONOTONICITY IN ECONOMETRIC MODELS (2012, methodology): “Econometrica 27, 585– 602. Lee, S., K. Song, and Y.-J. Whang (2017) Testing for a general class of functional inequalities. Econometric Theory, 1–47. Liu, R. (1988) Bootstrap procedures under niid models. The Annals of Statistics 16, 1696–1708. Mammen, E. (1993) Bootstrap and wild bootstrap for high”
• Nonparametric Instrumental Variable Estimation Under Monotonicity (2015, methodology): “Newey and Powell (2003) prove consistency of their estimator of the regression function g in the model (1).”