A PROJECTION FRAMEWORK FOR TESTING SHAPE RESTRICTIONS THAT FORM CONVEX CONES

This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure that has been barely harnessed in the literature. Based on...

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Bibliographic Details
Published in:Econometrica 2021-09, Vol.89 (5), p.2439-2458
Main Authors: Fang, Zheng, Seo, Juwon
Format: Article
Language:English
Subjects:
convex cone
Density
Economic theory
Nonstandard inference
projection
shape restrictions
strong approximations
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Summary:This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure that has been barely harnessed in the literature. Based on a monotonicity property afforded by such a geometric structure, we construct a bootstrap procedure that, unlike many studies in non-standard settings, dispenses with estimation of local parameter spaces, and the critical values are obtained in a way as simple as computing the test statistic. Moreover, by appealing to strong approximations, our framework accommodates nonparametric regression models as well as distributional/density-related and structural settings. Since the test entails a tuning parameter (due to the nonstandard nature of the problem), we propose a data-driven choice and prove its validity. Monte Carlo simulations confirm that our test works well.
ISSN:0012-9682
1468-0262
DOI:10.3982/ECTA17764