A Projection Framework for Testing Shape Restrictions That Form Convex Cones
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.
Cite
@article{arxiv.1910.07689,
title = {A Projection Framework for Testing Shape Restrictions That Form Convex Cones},
author = {Zheng Fang and Juwon Seo},
journal= {arXiv preprint arXiv:1910.07689},
year = {2021}
}
Comments
This version contains the following sections omitted from the published version: i) discussions of the examples in the main text, ii) proofs for Appendix C (in the online appendix), and iii) the complete set of simulation results. A previous version of this paper was circulated under the title "A General Framework for Inference on Shape Restrictions."