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A Projection Framework for Testing Shape Restrictions That Form Convex Cones

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  • Zheng Fang
  • Juwon Seo

Abstract

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 nonstandard 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.

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  • Zheng Fang & Juwon Seo, 2021. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Econometrica, Econometric Society, vol. 89(5), pages 2439-2458, September.
  • Handle: RePEc:wly:emetrp:v:89:y:2021:i:5:p:2439-2458
    DOI: 10.3982/ECTA17764
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    Cited by:

    1. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2023. "Constrained Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 91(2), pages 709-736, March.
    2. Isaac Loh, 2024. "Inference under partial identification with minimax test statistics," Papers 2401.13057, arXiv.org.
    3. Zheng Fang & Andres Santos & Azeem M. Shaikh & Alexander Torgovitsky, 2023. "Inference for Large‐Scale Linear Systems With Known Coefficients," Econometrica, Econometric Society, vol. 91(1), pages 299-327, January.
    4. Christoph Breunig & Xiaohong Chen, 2020. "Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models," Cowles Foundation Discussion Papers 2238R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2021.
    5. Zheng Fang, 2021. "A Unifying Framework for Testing Shape Restrictions," Papers 2107.12494, arXiv.org, revised Aug 2021.

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